One benefit of JWT as specced is that those APIs you pass it on to don't need to share an encryption key, which makes rolling the key without causing downtime impractical. With OIDC, for example, frequent key rotation helps you create a better security posture.
The benefit of signing versus encryption is many services are able to verify the authenticity without needing a shared secret. That includes untrusted services, which is frequently the case with OAuth 2.
You can encrypt a JWT token, but at that point it's not semantically a JWT anymore. It can be any JSON at all and doesn't need to match the JWT structure. The first and last parts of a JWT are a signing algorithm and signature, respectively.