You are remembering the pre-FM days of the 50's and 60's.Radio has already done this to an extent. I remember the days where a single station would play both Country and MOR music and also have non-music features in between. Now every station seems to belong to a single genre and even uses that branding in its advertising.
When FM started to become viable in the very late 60's and early 70's, most markets found themselves with triple the number of truly competitive stations. And if you write off the AM daytimers, in some markets the viable stations quadrupled.
So stations specialized. And record labels found profitable niche markets.
Harder rock found a home with "progressive rock" formats. Then that split with Album Oriented Rock popping out in the earlier 70's. And "chicken rock" which was later named AC came out in that early 70's period. Those are just a couple of examples.
All kinds of splits happened, and we ended up with boutique formats instead of department store formats.