Okami has a fair amount of puzzles, they're just mostly smaller to show the wider range of mechanics. Get ball into cup, bring vines to location, memorize dots on a page Simon says style. They're ultimately not too different from a puzzle you might encounter in something like A Link to the Past, or Breath of the Wild. Not difficult enough to be integral but enough to test your understanding of the game mechanics and later reward you for wit. Some of them also become very important for boss battles or speeding up fights with enemies.

Personally I never had an issue with brush move recognition, but I played both the PS2 and Wii versions and use a Steam Controller for PC which is the closest to the Wii's. Of all of them, analog sticks are probably the slowest, but keyboard control is pretty clunky for movement since it was intended for controllers. Combat on the Wii was something else entirely, it was genuinely meant for that I think as it has the blended analog stick + high speed but accurate input. For today, mouse input is very good as a very light trackball but so-so for a regular mouse - so the Steam Controller (or Deck these days) is a really good medium, or maybe the PS5 controller if you can use its middle touch thing somehow.

I'd say the only complaint I could make about the game is its pacing of the story. In terms of gameplay however, you take it at the pace you want to take it at. Don't want to fight? Avoid the scrolls. But fighting can be so fast, over in just a few inputs. Only a couple seconds so sometimes the winning battle screens themselves feel like they take longer (but they can be skipped). The isometric style during the battle rewards spacing and the byproduct is the difference in how the movement feels - it also plays into Capcom's general affinity for artificial difficulty, something like restrictions on camera movements and animation delays for Resident Evil and Monster Hunter. It's asking how creative can you get in this situation with these limitations?

I think the best analogy for battles with this in mind is to imagine each moment you freeze as the perfect image captured by an artist, but that can only happen when the demons are visible to the human (after Ammy stuns them). With that in mind you stun all the enemies then finish them in one fell swoop!

The game does have some pacing issues in the early game that could have been fixed by allowing to speed up if not skip cutscenes, but otherwise overall I think it nails the widening world adventure game for encouraging the player to really engage with the game engine and their wits to progress forward. I also think the early pacing does a lot for some of the revealing acts of the game, if it was fast and punchy the whole time then later elements like the events of the Ghost Ship of Heaven's Gate would be less impactful than they are. The stakes start out low as you familiarize yourself and they ramp up as you hit act 2. From there it's actually pretty easy to skip a lot of side missions as it streamlines you from there, unlike the early game where it can be harder to tell which quests main and side missions. Much like Twilight Princess where in the mid-late game it's really encouraging you to continue forward but if you take some time to explore you get experiences you'd have missed - although granted Okami is a little less forgiving with the gifts, with the 99 beads being the prelude to korok seeds I swear...

Anyway lol, tl;Dr I agree about the pacing although I think it's intentionally self indulgent on the story and the payoff is worth it and while the RPG elements you mentioned for battles are accurate, I would say that the speed and movement are more about spacing and timing. If you know the weak spot and the finisher, then each monster can be dealt with in 2 strokes, and placed well that can be the end of the fight right there.

Also not trying to discount your experience, just adding my perspective :)