Why does FM radio sound so good?

I have always compared my systems over the years to FM rock, etc, and, until lately, was always disappointed that I did not have that sound, even in the car.  What is the history of station playback equipment at FM stations?  I suppose it's all streamed or files now, but didn't they use single-song tapes awhile back?     
It used to be vinyl with 2 or 3 TT’s in the control room (the DJ booth). There was a large library with many thousands of records which were very worn and scratched until the Music Director would replace them, (very rarely). R-R tape was also used, especially to play concerts, interviews, and bands recorded by the station.

In the digital age the stations added pro CD players to the studio and spun between vinyl and CD. It took some time for the DJ to learn how to segue between songs seamlessly using CD players, but eventually vinyl was phased out and those libraries packed with records were abandoned.
Of course, early CD’s had that "digital" sound and many of us noticed. As hardware and software technology improved, FM radio then continued this way for many years.
Then automation and mainframe servers became the norm. The Top 40 and their network stations became automated and programmed from a central location, but Rock stations moved toward using files which were all catalogued on servers, although there were some CDP’s still in use. Now quality playback was consistent, although digital uses various compression rates and Rock/Top 40 stations use a high level of compression on their output before transmission.
You can hear the superior sonics of NPR/Classical stations vs. Rock stations, just as we can when listening to our music at home.
In today’s AOR/Rock stations, vinyl has been added into the mix. I laugh every time I listen to a certain station here in Philly when they announce they are spinning from "Vinyl Studio 1."

My career started in the late 70’s, so perhaps somebody can provide info on what the "old days" were like.

I can add to this. In the vinyl era, many radio stations also used broadcast tape cartridges for a lot of content: spots, promos, jingles, news actualities and music. These look like an 8-track cartridge, but differ because the rubber capstan isn’t part of the cartridge (it’s a part of the player) and they run at 7.5 ips. Typically, each cart had one track, whether it was a song or a jingle; many were stereo. The best of these cart players sounded very, very good, and they didn’t decay from wear like an LP or 45. There were stations that had all of their content on these carts. Carts were used on some radio stations well into the ’80s, and perhaps beyond.

Automation dates back at least to the early 60s, and early automation systems often relied on those carts. They were loaded into a carousel for spots, voice tracks and promos; the music usually came from reel to reels that contained cue tones to actuate the carts. Schafer was one of the manufacturers of these systems, and companies such as Drake-Chenault and Schulte produced content for them. They were extremely clunkly and imprecise compared to today’s automation.
Good call, Cleeds. Carts were clunky, but the later generation of tape decks used to rec/playback were first-rate. When making a promo or any recording, you would hit a button and a cue tone would be recorded into the tape. That marked the end of the recording, then the machine would cue up the tape for the next play.
Wisconsin Public Radio has an outstanding signal especially at home base in Madison . Took a tour thru the studios a few years back, thought
maybe those 8k pro Tascam CD players had something to do with it .
I know the least compression possible did .
Carts were clunky, but the later generation of tape decks used to rec/playback were first-rate. When making a promo or any recording, you would hit a button and a cue tone would be recorded into the tape.
Yup! The best cart machines had very high SQ. Carts also used a "tertiary" cue tone that could trigger a flashing light (very helpful on Top 40 stations to mark the vocal post or the approaching end of the track) or to trigger another machine.

I don't listen to a lot of FM these days. But when I do it sounds as 'clean' as ever. It does not have the frequency response of a class vinyl or even the best digital. So I figure as I age, I don't hear much more that what FM is capable of anyway. But the best stations, actually have some depth and space to them. 
In contrast to the horrid compression of satellite broadcasts. 
Classical and college radio sounds excellent thru my home system; clean is a good way to describe it. I’m using a vintage Denon tuner.
Rock stations sound good as well, except for the loud compressed bass.