As a fan of Old Time Radio, I'd love to hear radio dramas, comedy's, variety shows, etc. The problem might be that radio's prime time back then when this sort of programming was king was at night when those great dramas, comedy's, etc generally aired. Yes during the day game shows and soap operas(Helen Trent, Ma Perkins, The Guiding Light, etc) covered the airwaves on CBS, NBC Red/Blue, and Mutual as has been the case today with television (note how even TV is losing most of their soaps due to poor viewership as most women who are the target audience are now in the workplace leaving only the older retired women who the advertisers do not want left as the audience. Radio's prime time now is AM drive and PM drive where dramas, comedy's, variety shows, etc, probably are not a good fit.
What could possibly work, during drive times and possibly during the work day as well would be a modernized version of NBC Radio's "Monitor". Where you play popular MOR music with short news/human interest/comedy segments of only a few minutes in length with well known celebrities making short few minute guest appearances, the hosts on Monitor were generally well known folks from NBC TV (like Gene Rayburn of the Match Game, and Joe Garagola Today show and baseball fame, and some were well known NYC jocks like Ted Brown and Murray the K, etc. The production was professional and well produced. It was a fast moving show. So figure out what music that appeals to the prized demo today that would have a broad enough appeal as MOR music did back in the 50's,60's, and 70's when Monitor aired and come up with compelling entertaining short featurettes, and you have the 21st Century version of Monitor. That sort of entertainment might be workable during dayparts when most listeners are at work.
For the more long form of drama, comedy, etc, evenings would work better, but most folks don't listen to radio at night. Possibly on weekends as NPR seems to do fine with Prarie Home Companion on Saturday nights. So that could open a possibility for commercial radio to do more of that sort of programming, but the cost is probably not doable and a big gamble of pulling in enough listeners, whereas NPR is a special network that those sorts of radio listeners gravitate to and will financially support with their own money which is probably why they can do some of those cool radio things that the commercial boys can't touch.