I agree that GEB should be supplemented with formal study for a deeper understanding.

To clarify my anecdote, my "formal study" of incompleteness allowed me to manipulate the symbols, follow the proofs, pass a test, and conclude that incompleteness is something I have to believe.

By contrast, GEB showed me incompleteness intuitively. It made incompleteness seem natural and inevitable. It convinced me, instead of forcing my beliefs.

("There's a difference between a proof and a why", as I like to say.)

This is likely due in part to the fact that my "formal study" of incompleteness was part of university courses, and was not self-motivated. I like to think I could have gleaned a "why" from the formal proofs -- but I didn't. It wasn't high priority.

GEB makes it fun and relatively easy, which is a huge part of its appeal. That said, reading about something is rarely a substitute for hands-on experience.