WTF are you talking about?! I thought you were from Australia?
When was the last time you stepped foot in a comic store? DC, Marvel and other sanitised, superhero-centric trash does still command a lot of shelf space, but the superhero comic is otherwise definitely out of vogue.
I certainly don't read superhero comics (apart from the occasional, more thought-provoking take on the genre such as Invincible), or well, I didn't when I was collecting comics - that's a vice I haven't really indulged in much for a while.
But I still make occasional forays into comic shops and I can assure you, there is a great deal of comic goodness on offer that doesn't come within sniffing distance of any lame-ass cape-clad superhero creeps.
Check out Image, they're most definitely my favourite publisher and their output involves a wide variety of topics and themes. Admittedly, I can't remember seeing any comics about "regular people competing in teams", but that could well be because the subject doesn't interest me and thus isn't something that would catch my eye... and you also have to admit, that
is a rather niche basis for a story.
Edit: oh, you sneakily edited your post.
Wow anime plotlines sound as godawful as the art uh, there are plenty of "western" comics that don't revolve around combat/battles.
One of my favourite titles for a while was Drumhellar, which you could certainly describe as "supernatural comedy" or even romance.
I picked up an Image previews magazine the other day (recommended purchase actually, it's a pretty awesome magazine with a good glimpse into the comics world, especially for someone who's been out of the loop for some time as I have) and whilst the series displayed on the cover was something along the lines of a supernatural fantasy beat-'em-up with monsters, comedy and swords (still no superheroes to speak of!), the other series featured in the issue, with several pages of interviews and a preview devoted to it, was more of a romance.
My favourite comic of all time (in fact, my missing a few issues and falling behind in it was the main/whole reason I stopped buying comics regularly - I'm still waiting for the next collected volume of it) is Stray Bullets, which is a rather bleak... I don't know, crime drama? Romance? Black comedy? Coming-of-age story?... Yeah, I'd say the last one possibly fits best.
Definitely not any flashy, action-packed heroic silliness.
...Man, now I'm getting all sad about my recent lack of comics and up-to-dateness.