First, I said that networks would be carried almost 24/7. I don't give a damn what sort of time-fillers are aired on AM stations at night. Why would anyone be listening to an AM station when they could be listening to FM, or watching TV, or surfing the internet? The live shows in the early days of TV were aired only because the networks didn't provide content 24/7, so the local stations had to air something. As soon as more economical alternatives came a long, including expanded network feeds and syndicated programs, local origination shows disappeared. They were too expensive compared to the alternatives.
And yes, during the late evening hours, when most folks are watching TV, surfing the internet, or doing almost anything but listening to the radio, one station per market takes advantage of running Delilah After Dark. And other station do the same with On Air with Ryan Seacrest. Big freakin' deal. Setting aside the crap on AM, which is the best thing one can do with AM radio, you mention two whole syndicated radio music shows a few hours long. Both are often used as nothing more than a cost-saving alternative to having a local personality on the air. And of course, there are the hundreds of voice-tracked shows pretending to be local.
But I'm talking about national radio program networks that operate like TV networks operate now, or like radio networks back in the day, being the dominant content on most radio stations. Not just Delilah After Dark in the evenings when almost no one is listening to radio (relatively speaking, compared to drive times), but during all day parts. Locally produced content on radio will become as common as local content on television.