It seems to me, based on vague impressions of the times before me and about music I rarely listen to, that this is something old that is new again. Pre-1960 I can think of some names of singers, band leaders, and individual musicians. But no real bands (other than band leader names bands of course.) The band as the MAIN entity seems to start to rise late 50s early 60s. The main performer was the draw before that, the group around them not so much.
I just quickly looked at the top 10 songs for each decade, and "bands" seem to be higher in numbers in the 60s-90s, with maybe more names cropping up in the 90s. Before and after, names of people are in higher numbers. That's from a quick skim, not actually counting, btw.