Interesting points. However, I actually think Crash had the right set of moves in Crash 2. Adding the slide and slide-jump to the mix really expands the level of challenges you can include, including ones in Piston It Away and Spaced Out where you have to duck under obstacles and into enemies. Those challenges aren't possible with just jumping and spinning. Similarly, the secret lives in the Diggin' It bonus round you couldn't access without slide jumping. The body slam is rarely used, but allowed them to add a few secrets in Turtle Woods and Diggin' It. Also, I think those special crates might have been meant as a secret/puzzle to figure out how to break them, as there was no mention of them in the manual. And if you have sliding, you need crouch/crawl simply because if you slid under something but didn't make it through, how would you finish? You chose one of the few places where the slow crawling is actually needed.
In Crash 2, you can get by with just running, jumping and spinning through the entire first warp room (not with the gems though) and then can reach the game's first ending by just mastering run, jump, spin, slide I think. The bear had a simple control scheme, with the boost only required in the secret level (Totally Bear) and now in all levels to get the platinum relics. The jet board had a simple control scheme also.
Where I think they really expanded the control scheme and it made the game worse is in Crash 3. All of a sudden, you can just shoot enemies out of the way once you get the bazooka, and can even wait to go get the bazooka to go do the harder paths (except in Sphynxinator's blue gem path the bazooka isn't allowed on oil). It's a lot easier to maneuver your way around when you have double jump and death tornado spin.
Think about the Brio bonus in Heavy Machinery. It's hard because you have to perfectly space your jumps in a limited sense of time. If you had Crash 2's controls, it would be just as hard since you can't slide-jump off of a bounce. But if it were in Crash 3, you could shoot the boxes, then double jump and death tornado spin to the other side. Not challenging at all!
They really added the new moves in Crash 3 for time trial, but as the N. Sane Trilogy proves, you can have good time trial challenges without the special moves, and without levels specifically designed for it. Then later developers erroneously thought Crash was better with the special powers, eventually adding Tiptoe (useless), super slide (REALLY changed time trials), and rocket jump (eh, ok I guess). Fortunately the GBA games didn't have the bazooka.
First of all, thanks for watching! Secondly, you've uncovered my ruse. While writing the script, my memory lumped all Crash 3 abilities in with the Crash 2 ones. Only after some research did I find that I remembered that wrong, especially the double jump and bazooka. I didn't want to rework the Crash section to mention both 2 & 3, so I decided to stick with 2. I also thought about mentioning the jet ski and jet pack sections, but I wanted to cut out stuff I thought was distracting.
I do really dislike the crawl and body slam, but the slide jump always made sense to me. Except for that if the slide jump goes higher and farther than the normal jump, what's the point of the normal jump? :) It reminds me of Mario's longjump and backflip. One goes high, the other goes long, but neither replace his normal jump.