I'm not sure what kind of arrangement Joe Rogan has with Spotify but my understanding is he owns his podcasts and Spotify is paying him for the exclusive right to distribute them. So what does that mean for episodes they refuse to host?
https://jremissing.com has the full list of removed episodes. Joe can fight back and just have them hosted elsewhere.
Publishing elsewhere probably will violate Rogan's contract. Hard to tell without seeing the contract. Spotify might already have violated the contract by removing episodes, he might be due more money, be free to publish those episodes elsewhere, or be locked in to the deal. Rogan should talk to his lawyer about it.
I imagine he already is talking to an attorney about it. I'll be interested to see what comes of it.
IDK about US laws on copyright and authorship, but in many countries, including Russia, author rights divided into alienable and non-alienable rights. Alienable rights is rights author could sell or transfer to any third-party he wants, or by agreement - usually it is right to sell, distribute, earn money for the authors work. Non-alienable rights are f.e. authorship, i.e. nobody could change an author of work, right to do a work under pseudonym, and other stuff including the right for publication, i.e. making work accessible for audience. This rights under no circumstances could be sold, rented or somehow withdrawn from the author. So, if authors work is inaccessible for audience, author have a right to publish it by himself, whatever contract on the work he signed.
May be something similar could be found in US laws too, especially taking in account 1st amendment. Otherwise it will be very easy for any rich person who want to censor everything they want, just buying the rights on unwanted works and hiding them to silence authors. Obviously, Orwell 1984 or similar books rights already would had been bought out and books hidden from public due to "copyright laws", but they are still here.