Does anyone else in the NYC listening area remember WABC-FM back in the late '60s or early '70s or so? When I was a teen, I used to listen solidly to that station, as it played full cast albums all day, usually one per hour. (Yes, believe it or not.) I was so disappointed when the station changed formats (and probably call letters, too). I miss it to this day. I believe it turned into a country music station.
Around the same time, Lee Jordan on WCBS-AM had a Sunday (morning, I think) show called "The Sound of the Show." He used to interview Broadway personalities and play lots of selections from OCRs.
How I wish "regular radio"--as the original poster phrased it--resumed such programming.
As to HAMILTON, with each national exposure, I think the songs mentioned above could certainly find their way onto free radio playlists.