I love "typical" anime/ manga styles (big eyes, pointy chins, what have you...) and for most part draw in a style influenced by Japanese art due to that myself.
I don't care what others may think of that as I am used to being "odd" and will happily continue walking that path. It feels true to me. So, while some might say adapting a more Western style for my personal purposes would be more appropriate, for me it would be a lie.
All in all, isn't it just a style choice, lines on a drawing?
Unfortunately it comes with its load of associated baggage.
As far as I understand it, that's due to the visual tropes mentioned in other comments here but imho probably at least as much due to the (in)famous plot tropes like dense characters, fanservice, huge info-dumps, more telling than showing...
I see it as a huge opportunity for so-called "anime styles" that westerners use them with their own approach, mind you of course, using them purposefully without just copying Japanese tropes but bringing in an individual new perspective. That's why Avatar - The Last Airbender feels excellent to me. It's authentic in using diverse influences the authors experienced and all in all is it's own thing.
Manga/ Anime is inspired by Western art styles itself, you can see it in early developments most clearly but as time went on, mangaka again and again got inspired by Western imagery. (e.g. Mucha's art style seems to have oftentimes been used as an inspiration and Sailor Moon's author (heavily) referenced haute couture.)
Thus, I am sure that indie culture can bring some fresh air into the manga/ anime scene and widen the medium's definition. At the moment, it seems to be widely regarded as having limited possibilities due to the surrounding industry's state.
To be honest, I'd really like that to change.