Does anyone else have trouble with this; wondering why you started and continue to pursue something?
I think pretty much everyone has experienced this at one point or another. I used to have more trouble with this back when I was still a beginner and trying to find an art style I was comfortable with. I'd always compare my art to others (and still do sometimes) and wonder, "Why bother? I'll never make art like that." So, to answer your next question...
Do you sometimes feel like the output of what you made may never be able to justify the input of effort?
Yes.
If you do feel like this how do you cope?
I read an artist's advice once that said you need to balance out the time you spend looking at other people's art and your art. It's good to immerse yourself in other works because it can provide inspiration and you can really learn from analyzing those works. Sometimes I force myself to stop scrolling past every artwork and take the time to analyze all of the details -- how the clothing is shaded, what colors are used, the anatomical structure, etc.
But you can't just look at other people's artwork; you need to immerse yourself in your own too. And learning that has helped me a lot. Whenever I start to feel like my work is inferior, I keep myself from looking at other people's art. I go through my art folders and see the journey of my progress. I'll put on slideshows with my art and analyze that instead -- what I like, what I dislike, what I could improve on, what I've already improved on, etc.
And after that, I draw. Even if I can't draw anything I really like, I keep drawing until I've filled a few sketchbook pages. Because eventually, I get to a point where I am satisfied. It's like working out for me; my muscles might be stiff and sore to start with, but once I warm up and get into it, that's when I can enjoy myself and make progress.
I can't see myself stopping drawing anytime soon, but I have to say I've never felt myself be overcome with such a sense of "meaninglessness" towards my work. Any thoughts?
Don't forget that studying is just as important as drawing for yourself; it will help you feel better about your art when you can see the improvement. And I don't just mean studying from a book or reading a tutorial, but just studying artworks you like to see what you want to do differently. Finding the best method of studying will be pretty helpful (i.e. for me it's been classes, though I'm out of school now).
I had a long period of art block where I felt like my work was going nowhere, and it's because I was going through a depressive episode. I didn't have the energy to read any tutorials or look at a book or watch any art videos, so my art remained stagnant and I became frustrated. It was only when I started trying to actively learn again that I got out of my art block and became motivated to draw more, once I could see the little ways that I was improving.
TL;DR: Try to combine studying with personal work and spend time just looking at your art instead of comparing it, that's basically my advice!