Currently there's a voluntary "if you like us, find us on Patreon". Even being able to provide a "connect to Patreon" button on the screen would be a boost. UX and web site designers are well aware of how many people you lose with each step. Such a button could also auto-switch to the ad-free stream; I once paid for the upgrade but managing the different feed was a pain.
I'm still using Pocket Casts, so it's possible that an integrated app like Stitcher is already doing that. If not, I see a niche that would make it easier for amateurs to scratch out a living. I think the money is there if you make it easy for people to give it.
In practice, the wiring of everything together, the establishment of pricing, and (Shirky's argument) the mental transaction costs of having to decide whether to make constant small purchases has made this model very elusive.
I have no idea about the future of podcasting as a business. But, just as lots of people write with no expectation of being directly paid, there's no reason to think that lots of people won't continue podcasting in the same vein.
Unfortunately, besides Audible, most of the subscription networks (looking at you, Luminary) seem to offer the same genre of chatter/interview podcasts I can get plenty of for free.