I'm someone who learned declarative after imperative. In my experience, there are two things to understand about any declarative language: what it expresses, and what it actually does on the machine. The latter is often considered an implementation detail, but - at least for the people with imperative programming experience - it's actually crucial to gaining full understanding.

I remember my final breakthrough in grokking Prolog was realizing that the engine hides a glorified DFS that walks a graph of concepts for you. Suddenly, all the reasoning and non-deterministic features wasn't mysterious anymore, and performance-related implications became clear. Similarly, for people who struggle with async, it's beneficial to understand that async means somebody hid an event loop from you.

Both Prolog and Haskell make memory management really hard, and without good memory management you can’t reason about the run time of software.

Of course the solution is to learn a lot on the low level details of the compilers for these languages, at which point it’s not easier than imperative coding.

Doubt it. To do anything beyond basic stuff in Prolog you need to understand its resolution algorithm. And it is not enough to understand 'what' it does but also the 'how' which is basically a backtracking algorithm.

Yes! Being able to hide state is a blessing but sometimes also a curse. However Monads kind of allow you to hide/abstract over state too. I find it way more difficult though.