FMeXtra Tried This and Flopped
I don't believe HD radio ever attempted to use subcarriers. HD radio uses sidebands. Subcarriers are modulated directly onto the FM frequency whereas sidebands are on (slightly) different frequencies above and below the main FM carrier.
Although HD radio doesn't do this, the idea of using subcarriers for digital audio has been tried before with FMeXtra:
https://en.wikipedia.org/wiki/FMeXtra , putting a digital subcarrier above the stereo, and if a station is using it, RDS carrier. However, if a station wanted to keep its stereo and RDS subcarriers, bitrate was limited to 40 kbps. That's doable with modern codecs, but doesn't really allow for multiple decent-quality music subchannels. If a station wanted to drop all existing subcarriers and go mono, they could squeeze out 156 kbps with FMeXtra. Not bad, but most music stations wouldn't want to go mono for that. Besides, HD radio offers 96 - 120 kbps while keeping a station's stereo and RDS subcarriers intact.
Before I sound too much like an HD radio fanboy, HD certainly has faults that FMeXtra doesn't have. HD radio causes additional interference to adjacent stations, and completely wipes out first-adjacents, something that FMeXtra does not do. Though we probably wouldn't have seen as many subchannels with FMeXtra, there certainly would be less congestion on the FM band if the US picked it. Additionally, FMeXtra does not charge royalty fees like iBiquity (now Xperi) does for HD radio. And, since it's a subcarrier and not a sideband, the technical upgrades to FMeXtra are much much cheaper and less intensive than to HD radio.
As for codecs, FMeXtra uses some more advanced and specialized codecs than HD radio to make the most of its limited bitrate. FMeXtra supports HE-AACv1, HE-AACv2, and AMR-WB+ while HD radio only supports a (slightly modified) version of HE-AACv1. Though FMeXtra is legal in the US (since it's just a subcarrier) and a few stations still use it, the FCC picking HD radio as America's digital station probably sealed its fate.
I'm certainly not saying this is impossible to do again, but all new receiver hardware would be needed and HD radio basically serves the same purpose.