The idol industry is disgusting and I'll never support any anime that colors it as something happy.

I assume it's a nod to the source material or something? "Yeah, we remember you guys! Remember this?"
Uma Musume is a very popular gacha, obviously, and the stuff I've seen uploaded about it seems heavy on interactions between the girls and the trainer or coach or whatever the player is supposed to be. Girls looking cute/sexy and dancing is definitely part of the gacha playbook.
I liked Oguri Cap's original dance, it showed her awkwardness and stuff but I guess this is part of character growth and becoming a real Uma Musume. But, she lost part of her soul... I guess that's the idol thing. I hope she's able to hold on to her quirks.

i don't know how it is in the games but we've seen it tied directly to oguri's development AND it's clearly there to appeal to otaku who are into the ideal of the multiperformer idol
it's not that important, most of the biggest developments took place either in a race or right after it and before the idoling, the act itself doesn't take up much time, more of a symbolic thing

Concerts were an important part of season 2.
Teio's initial victory concert was foreshadowing both Teio's continual struggle with injury and her evolving interpretation of fortune and fate. The interruption of her goodbye concert was what led to her trying one more time. And concerts show off Teio's dancing ability, which was also a characteristic of her IRL counterpart.