If you’re a hobbyist, you might go “oh no, this won’t work out, Overcast users can’t see my podcast” and switch hosting providers.
If you’re going into podcasting as a business, don’t skimp on having a lawyer review the things you’ll be signing up and paying for, and if you skimp on that and get unlucky, expect to be doing the work required to move providers if what you signed up for isn’t satisfactory. It’s really that simple. This service costs this much and has these limitations, that service costs more but doesn’t have those limitations.
So yeah, when you sign a service agreement, expect only exactly what the service offers in the agreement, and if the terms are not satisfactory, go sign with someone else. What is the issue? If I can’t find someone’s podcast in Overcast, I’m simply never going to consider even listening to it. Conversely, some podcasters are actually okay with that and would prefer to pay for cheaper hosting. That’s a valid choice for them to make too, but they are making a choice whether they pay attention to it or not.
Also: just a note, this is only a hosting issue. You can still list your podcast in the iTunes Podcast Directory (or whatever it’s called now) without hosting on Apple’s servers.