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.
Oh, it definitely dates it - but you can have music that wouldn't have as much of danger of that.
The real problem is the attempt to be cutting edge. Any time that's done, a show ends up being dated, and often really, really quickly. Consider, if you will, The Mod Squad and Laugh-In. Very hip for their time. Cringe-inducingly dated now. Hell, just look at SNL's musical guests from years back, particularly the 70s. Leo Sayer - eek!
Hence put out something unplugged, very low key. Not the next (or current) hit for anyone.
Not Culp (or Hayes) of course, but something like this. Something that does NOT look pro.