When I looked up what they do and how to get them, I realized that people don't seem to care. Or at least barely (myself included). Probably because they're not tied to anything.

If there was e.g. some unlockable permanent thing (whether a functional item or something cosmetic for future runs or a new game+) or leaderboards for the number of medals one has collected or at least an achievement - or maybe some combination of multiple of these - players would have reasons to care.

Although I gotta say - that idea of it enabling gameplay benefits... might feel very grindy and frustrate players. It's of course a question of balance.
(Damn, this reminds me of something I forgot to mention in my review - that the game feels very well balanced. Such a shame one still can't edit reviews here...)