How important it is to have accurate perspective/proportions, imo, depends on the tone of your comic! Some stories/characters/environments look bad if they're "off," others look fine as long as they're consistent. Tons of successful cartoons have perspective and anatomy that's far from accurate, but they still feel solid and readable, so it's obviously possible to make an unrealistic style work!
How important is it to have non-distracting perspective and proportions? EXTREMELY important. Having a style that isn't realistic is cool! But if it's off in a way that's distracting, in a way that hurts the effectiveness of your story, it's gonna detract from your work.
I don't think there's any easy measure of what is distracting and what isn't. I think on some level, it's the old saying about how "you have to know the rules before you can break them" -- once you understand anatomy and perspective very well, it's easier to be loose with them in an effective way.
I'd say to any artist, it never hurts to learn and practice the rules! I can say from experience that when I started trying to construct my figures better, it did make my work more stiff -- at first, because it was something I wasn't used to. The more I drew that way, the more comfortable I got. Same with perspective -- my oldest drawings with an attempt at accurate perspective feel very halting, but now that I've drawn with perspective a lot I feel much more comfortable with it, and don't feel like it stiffens my drawings like it used to.
There's deeeefinitely merit to drawing your comic in the style that's most comfortable to you! but outside of the comic, when you're just sketching and practicing -- I would say, don't be afraid to push yourself (and your style) to get more comfortable with the things that feel restricting!