I'm not affiliated in any way, but Pocket Casts has been running for years and is an excellent option on both iOS and Android. I know there are some other good options on Android as well, if Pockets Casts isn't your thing for some reason.
But to be listed on Google Podcasts, they consume your RSS feed and upload it. The terms include the standard granting Google irrevocable worldwide royalty-free rights to your intellectual property and includes highlights like their ability to use your podcast content even if you remove it from your feed later.
Since most other podcast apps don't do anything but help others find your RSS feed, I've never had to agree to terms and prove my ownership to be listed anywhere else, Google's demand of IP rights seems unique in this space. I've actually found my podcast listed on all sorts of sites I've never heard of with no such terms required.
I'm not too worried for myself since I plan to release it all in a Creative Commons album anyway, but I'll keep it in mind if I see someone talking up Google Podcasts.
I don't understand why Google refuses to accept standard podcasting convention and let users consume my RSS feed direct and download my show from the servers I've provided.
For iTunes, as a counter example, de-listing InfoWars will hurt their discoverability obviously, but their listeners can easily subscribe themselves manually in the iTunes client.