The issue with JWT in particular is that it doesn't bring anything to the table, but comes with a whole lot of terrifying complexity. Worse, you as a developer won't see that complexity: JWT looks like a simple token with a magic cryptographically-protected bag-of-attributes interface. The problems are all behind the scenes.
For most applications, the technical problems JWT solves are not especially complicated. Parseable bearer tokens are something Rails has been able to generate for close to a decade using ActiveSupport::MessageEncryptor. AS::ME is substantially safer than JWT, but people are swapping it out of applications in favor of JWT.
Someone needs to write the blog post about how to provide bag-of-attributes secure bearer tokens in all the major programming environments. Someone else needs to get to work standardizing one of those formats as an alternative to JWT so that there's a simple answer to "if not JWT then what?" that rebuts the (I think sort of silly) presumption that whatever an app uses needs to be RFC standardized.
But there's a reason crypto people hate the JWT/JOSE/JWE standards. You should avoid them. They're in the news again because someone noticed that one of the public key constructions (ECDHE-ES) is terribly insecure. I think it's literally the case that no cryptographer bothered to point this out before because they all assumed people knew JWT was a tire fire.