From my limited understanding (and what I just read up right now), if you send audio through non-flat-response speakers multiple times (so stick a mic in front of the speaker to re-record it, and play it back through the speakers again) then each time your highs and lows would become more silent and the mids would become louder.
They're designed as the last piece in the chain, to then give some artistic coloring to the music.

Flat response is designed to not do that, so that what comes out sounds as much as possible like what you've put in.

In my personal experience as a very hobbyist musician, yes, of course I will also try to listen to my shit on phone speakers and try to make it not sound entirely terrible there. But you go from one consumer-grade speaker to the next and entirely different frequency ranges are fucked up.

Having some headphones that don't fuck with the sound (whether intentional or just crappy) is really helpful, because they give me a middleground that's likely to sound reasonable on multiple systems.
Much better than composing on a system that fucks it up in a specific way and then playing back on another system that fucks it up in a different way. That's pretty much guaranteed to sound terrible.