I think the IDs were always indended to identify a particular transmitting station, not necessarily an ownership chain or franchised format. In order to be able to identify the point of origination on the frequency you're listening to. For any number of reasons. And with so many simulcasts and translator networks now, it seems even more useful to know what you're actually listening to.
The ID rules also help to reinforce the "obsessive compulsive" nature of a lot of radio folks.
I once worked at a station back in the days of LPs, where I played an orchestral/choral version of Handel's Hallelujah Chorus to finish out the hour I was hosting, to end at midnight, before the overnight guy took over playing the music. But the backtiming was off by a few seconds. The overnight announcer still felt he had to do a fast fade just as "Messiah" was finishing on its glorious high note, in order to start the recorded 20-second legal ID cart right at Midnight on the dot. Assuming the clocks were all that accurate, anyway. (The station had no live network programming.) It was a real lesson for a young broadcaster in how easy and eager stupid people can ruin a beautiful moment for listeners.