This idea was something we, a group of college students, felt was missing from our social interactions. I agree, it's a bit clunky to set this up mid conversation.
I, personally, find that this works really well with existing friends or when forming new friends online through things like Instagram or Tinder.
To your point, we're always looking to expand our use cases and reduce the first time friction.
Starting off, we focused heavily on comparisons but have branched out since. For example, the stats page you're first taken to gives you some analytical information about your own music. Strengthening out this page with things like music evolution, recommendations, rankings, &c is foremost priority.
Currently, we have friend links that deep links into creating a friendship (e.g. mine is https://smtn.es/125.ferda-bruh). Pivoting this to share your statistics and music tastes is an interesting idea -- it definitely helps introduce the platform to new users and personalise the platform for existing users.
I'll propose it to the team, thanks!