I think that's a dumb reward that makes no sense. Suddenly, if you can play 1 song, you gain proficiency? I mean... I guess. Maybe. If you've been practicing it all Day, maybe you know the very basics.
But then, how'd you play the song to begin with if you aren't proficient? 2 Performance checks? Yeah. It's kinda weird.
5e has a few backgrounds that come with instrument proficiency. Why not simply add it to them?