Long before JWT existed, if you wanted to pass some trusted data through an untrusted channel, you would make a payload with an expiry, encrypt or sign it with your secret key, then send it. However, you would need to make up your own way to send this info. For example, if this were a website, you might dump the signed/encrypted payload into several form fields and upon receiving it back, you would verify that it was signed with your key.
Now that JWT exists, there is a standard way to do it so you don’t have to write the same boring code a bunch of times in different languages. You just have one string you pass in one field and if you tell someone else that it’s a JWT, they know how to parse it. You don’t have to document your own special way anymore.
At the end of the day, it’s just a standard for that specific problem that didn’t have a standard solution before. If passing data like that is not a problem for your use case, then you don’t need the tool.
To use your Protobuf example, there was a time before Protobuf or tools like it existed. I can tell you that writing the exact same protocol code by hand in Java, PHP, and Python is absolute tedious work. But if it never came up that you had to write your own protocol, you neither know the pain of doing it manually nor the pleasure of using Protobuf, and that’s fine.