Not sure if this homogenous writing applies to contemporary traditionally-published YA books, since I haven't read any. But I think another aspect is that a lot of online works come from younger writers who haven't read a large breadth of books from different genres. They simply read other online works and so the "samey" beast feeds itself.
I can definitely attest to this homogenous writing problem. Honestly half the time I turn Grammarly off because I hate their suggestions, especially if I'm doing a dialogue-heavy scene and my characters aren't exactly "proper". I like @therosesword 's idea of writing "like myself", but when I do take inspiration I try to do so in terms of learning how to apply things to my writing. I've always loved the Douglass Adams quote "he flew through the air in much the same way that a brick doesn't", but all that did was make me mindful of just how much strength there is in thinking about how you can paint the picture in your reader's mind. If anything, we should be learning what tools we have at our disposal, not how other people use them.
I agree with you! I personally don't use these writing programs. I know that they can help with grammar and punctuations, but I think they remove that "special touch" your story would have. After all, it's your story, and in my opinion, when you use programs like Grammarly or ProWritingAid to "improve" your chapters, the style of writing you put in your chapters would just... fade away.
Honestly, I think your satisfaction with your chapters is more important than punctuations. If you write chapters without using any writing programs, it kind of makes you feel great, and you would get really motivated as well! (although I don't know if every author feels this way, but I do)
As you can see when you use these programs, the suggestions in Grammarly or any other writing software aren't quite accurate; what I mean by this is... they don't wholly understand your story. If you're focusing on something heavy and emotional on your story, they would still correct your grammar, but they can't help you highlight the impact you really want to bring to your audience. These programs can definitely help you with your grammar, yes that is true, however, they can't help you emphasize your story. They can improve your grammar, punctuation, and sentence structure, but they can't really help you with your novel itself, if you get what I mean.
It's just like what they say, no one knows your story more than yourself.
I use it as a back up check and ignore/double check whatever corrections it wasn't me to make that I don't agree with.
It really hates my fragmented sentences 
Definitely suspect it's a case of writers reading what's popular in their genre and (knowingly or not) emulating it.
I do this too, though I read a lot more physical books than webnovels, and the variety of genres I read has done some kind of odd things to my writing... When I was writing my novel I noticed that it got sillier when I was reading Terry Pratchett, and more descriptive when I was reading Dickens. It still sounded like my voice, but it's hard to deny the influence of what you're reading, even if you're really not trying to emulate.
I can definitely attest to this. Weirdly though my tone seems to shift even between my short stories. I feel like the tone I'm going for changes my style very heavily, as does my mood.
Examples- These were written only a few days apart:
When traveling in Aphing, there is nothing more important than choosing a good tent. It should include a nice ground tarp, made from thick, sturdy canvas to keep the water and the mud from seeping in, and a strong structure that is light in weight for travel. The knights of Aphing often travel in groups, with heavier, four-walled tents to house multiple soldiers, and a much larger, much heavier tent for their commanders to sleep in luxury - often carried by the lowest-ranking soldier. This was often the cause of severe back pain for new recruits, but that was a sacrifice their commanders were willing to make. The nicest tents were spacious, well-insulated, and thick enough for a sharp dagger to get stuck in.
Forista’s tent was a sheet of canvas hung over a rope.
Compared to this entry for my lore series:
It is in the best interests of all those that pursue the secrets of the world, that one should start with that which lies in plain sight, for one cannot hope to understand the occult without first looking the world in the eye. This is where the knights fail in their quest for enlightened glory. Their shunning of magic and all that lies within it is blinding, and leads only to self-serving pretense. So too do the mages suffer, choosing to seek only that which they cannot see. The greatest blind spots often hide directly under one’s nose, and no amount of study will help those who refuse to open their eyes. Worse still is the Council of Magi, the grand wizards of the Great Shielded City of Stockholme - trapped by their own self-importance, and unable to see that their spiritual enlightenment is merely a method of self-congratulation. They seek knowledge only with which to scoff at those they deem lower, and their worship of the self will be their undoing.
Different tones, different styles, and honestly just a different mood from my perspective.
I never used this kind of program for English, but I had a trick to check the 'uniformizing effect' of such a program for French: feed it extracts of different styles I liked in classic literature (can be also done with good contemporary things obviously).
Seeing programs try to correct what makes you like the style of an author is a good way to realize, then detect why and when, this kind of program is overdoing its job.
I think they are helpful, but we should always remember we are the ones in charge.
I can see that happening in the same way that standard English classes enforced grammatical rules. But they were preparing us to write for mere communication; that is, to express ideas clearly. But writing fiction has a different target. It wants to paint images and entertain and sound like real life.
I use Word mostly & it seems to me that it hates it when I write dialog the way that people will actually speak. Partial sentences. One-word sentences. Numerous pauses & passive voice like nobody's business. I pretty much only let it remind me about mis-spelled words.
I don't think programs are making writing more homogenous, or that writing is more homogenous than it was 100 years ago anyway.
If you're reading a lot of cheaply written genre fiction (and most of web fiction is this), you are going to run into this issue just because the stories aren't written with incredible desire for ambitious prose in the first place. Literary fiction is just as well-written and riveting as it was in the age of Oscar Wilde and F. Scott Fitzgerald, it's just that those aren't the kinds of stories that hit it big with audiences anymore.
Yeah, I cant lay indifferences or lack of originality/creativity in writing on a program; that is on the writer and their approach versus who they are writing for.
I think the sense of homogeneous with writers using the programs relates more to how the writer uses the program. You could have written a killer scene with awesome dialogue and stellar descriptions and then the program starts finding issues. Some people trust that the suggestions to be correct and edit away. The originality and spark can be lost in the edits which can make the story seem off despite being grammatically right. Even dialogue starts to feel the same if everybody is using perfect grammar.
People using the same tropes and plotlines to write eerily similar stories is another issue.
I'm honestly not even sure if that's happening either. People are using Grammarly to fix grammatical weirdness or take their suggestions for style and the end result may not be good, but I imagine in many cases the original writing itself wasn't particularly good either. It's bland but it's not worse than it was.
Maybe, maybe not. My point was more along the lines that people don't start publishing fiction online because they wanted to produce quick fiction. We also have our writing dreams. Some people may overuse the tool and we get sentences like "her mouth felt open" (real suggestion I got) or dialogue that sounds the same, for example, instead of taking time to hone their work and make it better.
I tried using Grammarly, but I just didn't like it. ProWritingAid has helped me a lot with grammar issues I overlook while editing, but personally, I've found that the best way to fix chapters is by having reviewers/editors look over the work.
Yeah, there's certain weird things that these programs like to "fix" which don't really need it. But I'm not sure if it's solely the program's fault. It could just be new writers are taking inspiration from such style too, especially if it's been used in popular stories.
I just use it to check my spelling a bit, considering I'm not a native English speaker. Usually I can write sentences without a program though
Oh very true. It's the first time I ever used one though, so I hope I can learn more of it and improve a little more myself. 
I found using them often makes my story feel very robotic and loses all of its personality.
I only really use them for any spelling errors I may have missed.
I think different characters in novels benefit from different dialog structures. I nearly broke Grammarly with my novel, The Faerie Dusters. One of my characters speaks in heavy southern colloquialisms, and I wanted to show that phonetically. Got dinged over a hundred times for one chapter alone. Otherwise, I find Grammarly very helpful in finding the double-the mistakes and all the and missing the final d mistakes. And of course, it helped me spell colloquialisms. 
As a tool I think it and other programs are great (like I said, I suck at grammar) but I find, sometimes, when I'm reading the writing takes on a "robotic" type feeling, like @steffiemusings said.
That's where I think people might be in a hurry and a suggested line comes up and "that'll do."
"That'll do" always reminds me of my father who used to say "good enough... isn't"
But, it's up to the writers and I think, from what's being said on this thread, most are using the "tool" aspect in helping with grammar, spelling and punctuation and applying their creativity in ways that might make Grammarly and other tools like it be the new game of not turning left and hearing the words "recalculating."
