Every independent podcast I listen to relies on people paying for various premium features via Patreon. I've supported a few of them a few times, but I always stop because it's an awkward relationship... you listen to most episodes in one podcast app, but then you have to use the crappy Patreon app to listen to the paid content.
I've subscribed to three podcasts via Patreon, and I've successfully added them to Apple Podcasts and Pocket Casts. (I use one for music podcasts, the other for talk, so that I can have different defaults / different use cases).
Most Patreons I've supported seem to expose an RSS feed, and you can simply add that to either system. (Finding the "manual RSS feed" in Apple Podcasts is a bit of a pain, you have to go to your list of podcasts and then find the Edit button at the top of the app, and the option appears.)
I agree it's not nearly as seamless as the Apple / Spotify solutions, but take another look at your Patreon subscriptions; you may be pleasantly surprised.
(Note that Apple, because of its App Store podcast model, doesn't actually share your email address with creators, so they can't send out any bonus content that's not embedded in the podcast.)