The issue is that Green Flower doesn't even manage to sound peaceful, its just flat out boring and gets annoying to hear over time, and doesn't fit the pace of the game-play. 'Catchy' has nothing to do with being a good song, catchy is just a way of getting a song to stick in your head for an extended period no matter what the quality of it is; if catchy and repetition alone were a good thing, then Sonic 4's soundtrack would be a masterpiece.
The super theme is the most mellow and repetitive ear assault I've ever heard, coming much closer to Sonic & Knuckles' invincibility theme than anything in the contest of most irritating tiny jingles. Yeah its pretty hard to be mellow and at the same time assault one's ears, but it manages to by being being the least dynamic song in the game, while also being one of the shortest; and to add onto that you're forced to listen to it for a minimum of fifty seconds, nearly a minute. A super theme should be suited for 50 seconds or higher. A short jingle is made to be used for a short period, what we have now is like listening to the starman theme ring for two hours. This is one of those areas where SRB2 didn't need to mimic the classics when it could do better, just because they had tiny jingles that were remixes of the title screen's tune doesn't mean it needs to do the same.
I never said Sonic had to be defined by guitars and brass or even implied it, other instruments can be put to great use or at the very least sound high quality. I've even heard Sonic games commonly using things like violins in the instrumentation.
It's not like the development team doesn't realize this though. I'm sure the issue is that they have no willing members to compose new music for them, which is the bigger problem. Then again there's tons of willing Sonic fans all over places like YouTube and SonicRetro (here it comes :D) with tons of talent that could be put to use on the team if they just searched out for them. So eh, I don't even know.