JWT doesn't encrypt (by default) the payload. The header & payload is passed through base64 and appended with a hash to produce a JWT. JWT verifying doesn't require making API call, and is essentially a hash check. Any verifier with a public verification key can determine if the JWT is bogus by a quick hash check and reject the request right away.

Comparing to session IDs, you have no way to know if an unique id is bogus or not. You have to check from a list, be it a cache or a database. This limits the scalability of the solution. I'm not an expert, but AFAIK JWT verifier can be stationed on the edge of the application network, and I have not checked this but I suspect they can even make a hardware solution for those kind of activity. That's definitely a big reduction of attack surface in terms of DDOS.

IMO JWT doesn't have that many moving parts. Encryption parameters are handled by libraries according to tested standards. The only real thing you need to do is to keep your private key safe.