The whole idea is rather odd, but it's not like there's never been music in Trek that goes outside of theme songs and incidental music. I think what I dislike the most about it is the concept of it being a regular thing. Why not have it, but as a rare occurrence? Bring in whoever - dress them up as crew members and make it some sort of - the crew is getting a well-deserved break - or whatever. Hell, I actually write a pair of E2 crew members as playing guitar and singing because you've got a century to kill so why not do a little coffee house kind of act? But it would have to be small.
They learned their lesson after all the bad singing by the hippies in "Way to Eden" which terribly dated the series.
That's the reason we only have classical and Jazz music in TNG.