I got about 200 pages in, and just could not continue with it. 'incomprehensible mess' would perfectly describe my sentiments.

As having taken undergrad/grad courses in logic and set theory, any interesting nuggets about recursion/completeness/incompleteness/etc that one could glean from GEB can much more coherently and succinctly be obtained from a proper book on logic/computability.

The counterargument would be that this book is meant as entertainment: from my experience with the first ~200 pages, it was a complete chore to read, as ideas were presented enigmatically and slowly, to the point of frustration. Granted, my attempt at reading it was almost a decade ago.