Fair criticism.
Oh, I like to ponder such thought constructs. Ever wonder why ghosts can walk through walls but do not fall trough the ground. The answer is of course, "magic". It does not follow regular rules. But if you make your super power be a mechanic, questions arise. Like why that awesome ability is not used in other circumstances. You could of course make up all kinds of additional rules, like ghosts could do it, but they do not think of it. Or you could just stay with the "magic" explanation.
Of course exploring all the side effects of a mechanic can be fun in a plot. But more often leads to situations like in that Star Wars movie, where they finally decided to apply real phyiscs combined with available tech. Ramming a thing with very high speed. That is a break from the usual magic explanation for tech there and leads to the question, if this is possible, why did they not destroy the Death Star(s) with that. Or planets for that matter. Why build a Death Star in the first place, if you can just accell a drone ship to near light speed in the direction of your target.
Oh, btw, the concept of changing view in a puzzle has been seen lots of times. Either you change your char, the view or even both.
The more abstract puzzles like this one here can get away with 4d, but in the usual platformers, that would be hard.
I even remember a time puzzle in that old point&click Day of the Tentacle. You had to change stuff in the past to solve puzzle in the present.
If you can pull it off, a new mechanic can be awesome. Portal comes to mind.