In my view, learning the basics of Prolog is very worthwhile, irrespective of whether you'll ever use it in the real world. It's also very worthwhile to understand the basic ideas underlying unification, and how a (trivial and inefficient) implementation might be handled.
If you have a problem that would be best solved using declarative logic, you should ideally recognise that and know (if you have the choice) to use the right tools for that job.
However, I agree that Prolog needs a very different mindset from conventional imperative languages, and also a very different mindset from functional languages. Beyond a certain point, it appears to require a lot of experience (just as with anything), and there's even a lot of "textbook" knowledge that makes my brain dribble out of my ears.
My impression is... we are probably both missing something special to a degree, but it wouldn't be practical to dedicate the time to learning even a reasonably complete textbook-level knowledge for Prolog, let alone trying to develop real-world experience, unless you're considering a possible logic programming career.
I've recently been reading a book on AI and expert systems published in 1989 - a lucky find in a second hand bookshop. In significant part, it's a specialised tutorial on Lisp and Prolog. True, most of what it covers hasn't been that impressive for quite a while (search, heuristics etc), but it's still very interesting, and IMO a worthwhile thing to invest a bit of time in.
More recent books that specifically describe Prolog would be better for learning the language, but the risk then is that your brain will dribble out of your ears somewhere in the intermediate-to-advanced material.