Then, you'd get rewarded for a super awesome roll.
That is the point ...
Right now, you are rewarded if you act acordingly to your characters ideals and preferences.
Then you would be rewarded for what exactly?
What even rolls represent ... "your thief was inspired by the extraordinary quality of his own lockpicking skills" ?
As a long time DM, there is nothing players love more than getting rewards for even the littlest things. I've had more than a few players say things like, "I rolled a Natural 20 on my skill check. What do I get for that?" This in more games than just D&D. In old school Star Wars, it was Force Points. In Lord of the Rings RPG it was Courage. Call it what you want, players like getting special points for good roleplaying AND really good dice rolls.
And there is no better use for these things than combat. So, I agree with the OP but only of they allow Inspiration to be used in combat so we get more opportunities to use it than skill checks. Again, take away height as an advantage and allow inspiration in combat. Then, 4 Inspiration will almost seem like not enough, BUT that allows Larian more flexibility to reward players more with Inspiration which provides a more rewarding gameplay.