I disagree that it is “quite approachable for the non-expert” assuming you meant a general audience without a background in high school mathematics. They probably wouldn’t exactly understand the Löwenheim–Skolem theorem or ZFC, or consistency arguments and so forth as presented in the book.

Some parts require more math than probably the general audience will be able to grasp but if they gloss over those sections they could still get the gist of what follows.

I think I’d rephrase it as “quite approachable for a talented high schooler / someone with knowledge in undergraduate mathematics”