This question is also complicated by the fact that virtually all radio stations nowadays use lossy compression extensively in their production process. So from a quality standpoint, it really could be far worse than you might think.
Jukebox software using Musicam/MP2 (!) has been standard for quite some time now - I remember seeing a Windows box with a sound card control all the programming on a station in 1992 or so, with a 9GB RAID array for music storage. NPR, if I'm not mistaken, still uses MP2 for its satellite feeds. The BBC has taken great pains to ensure a lossless signal path to the station, although it's typically compressed to hell on DAB anyway.
Nowadays I understand that syndicated content, and even individual music singles, are transferred over FTP, typically using MP3 or something of that nature. And it's entirely unclear what bitrates and encoders they're dealing with.
Ultimately, this hobbles the sound quality of HD Radio. The bitrates I've seen for it are great, and soundly beat XM/Sirius down - but virtually everything played on radio is already lossy compressed. So digital FM radio generally requires a transcode! Not good.
Your information is quite dated. The need for lossy compression for digital audio storage in broadcasting went out in the late 1990s. Musicam...never really got started. MP3 is really MP2 layer 3. We used high-rate mp3 when large SCSI HDDs were expensive. Those days are long gone. In the early 2000s the "norm" was uncompressed broadcast .wav files for music libraries, possibly .mp3 for commercials because they arrived for air-play done that way already.
Today when MP2 Layer 3 (MP3) is used, it's generally at 256Kbps or higher, and results in files indistinguishable from the original. There are situations where low-rate compression gets aired, but it's not the norm any more, and isn't why radio stations sound different from each other.
Studio-transmitter links are minimally lossy at worst, more typically lossless today. The "hobbling" of HD Radio (no such thing as digital FM, sorry), is in that the total available bandwidth can be divided into several sub-channels. If HD1 only is used, the results are pretty darn transparent. If the station elects to use many sub channels, there must be progressively higher bit-rate reduction, with the highest quality still presented on HD1, but never as good as when that's the only digital stream transmitted.
It would not be correct to say, "virtually everything played on radio is already lossy compressed", however.
The one mandatory transcode is into an HD Radio transmitter. But that transcode doesn't hit analog FM. The presence of an HD Radio signal does degrade analog FM slightly, but not in terms of transmitted audio bandwidth on analog FM.
Far and away, the most damage done to a broadcast signal occurs in the broadcast processing chain, not the storage and transmission of the audio.