Is it necessary to encrypt a JSON Web Token more than what is built-in?

As a developer I do have some understanding of OWASP, I am also a member of OWASP community, official due paying one. Anyway, what I may not understand is information security in that I am not a security engineer and so I pose the following question:

Is it necessary to encrypt and encode a JSON Web Token?

In my experience, no secure or confidential information should be in a JSON Web Token anyway, outside of the id and email of the user. I can imagine a customer such as a bank freaking out about that, but what can someone do with an email? The password is salted and hashed and also at least in the NodeJS world that is my wheelhouse, JSON Web Token is tamper resistant.

I can verify that a token was valid by using the signing signature and if it fails due to tampering then the services will no longer trust it, that simple no? Why would it be necessary to encrypt it, Encode it And whatever else an overzealous engineer can think of? What problem is it solving or what use case is it handling that is not already built-in? Is it because in other programming languages there are no libraries built-in that can run a jwt.verify() on the JWT?

Could the case described in this post be what the institution is trying to solve?

JWT(Json Web Token) Tampering

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Author: Daniel