> the ridiculously high number of possible permutations doesn't matter at all in practice.

I'm not sure I'd go that far. For the most part, the difficulty level of twisty puzzles does tend to increase with the number of possible permutations. The big things I can think of that break up that tendency are jumbling and bandages.

It's just that the number of permutations doesn't give you a good intuitive sense of how difficult a puzzle might be.