Yes! This would make addition to (at least) the entertainer background. (Maybe if you a Bard entertainer you get perfomance proficiency at level 1).
I wonder what other background it would work for. Maybe Urchin?
Should the soldier background give a weapon proficiency, then?
Entertainer and Outlander give the instrument proficiency in 5e. So, if you are a Bard and Entertainer, you'd get 2 instrument proficiencies instead of 1.
But Performance Expertise makes sense as an alternative. I do like it.
I'm not sure about handing out proficiencies, though, like weapon Prof for soldier. Once you start doing that, it starts breaking the balance.
