People care. If the band is grooving, entertaining, giving people a good show and dance party, they will appreciate knowing the name of these hard-working musicians on the stage. It is a big mistake to not introduce the band. I have insisted every band I play in adopts the practice in some way and does it quickly at least once a set. Special solos deserve another shout out. It doesn't need to be a big production with spotlights and solos, you can go 'round the world and quickly tell everyone who is playing what. When I play in a band that's cooking, each member gets a round of applause after their name, further proof people care.
Not only that, I think it is a nice way for the BL or lead singer(s) to show appreciation to the hard-working musicians in the band.
I sub'd for a band recently at the Baker Street DTC. It's a pretty good gig, decent pay, one you want to protect once you get on their rotation. BL failed to introduce the band, not even once, and never said a word about appreciation for the the wait staff. Terrible way to build friendships.