Wheelsets/ Rims road, gravel lateral and vertical stiffness

[wheelsONfire]

Looking at rims/ wheels i think i have come to see that most of us learnt wheels should be stiff.
But i've been feeling, some are simply too stiff, which make ride feel on the harsh side.
How do you guys feel?

Does stiff wheelset always translate in to better acceleration?
If yes, what more is so great?

Seems strong sprinters may hammer out incredible power, but for those that aren't near this, ..
do we have any gains from a super stiff wheelset?

Mainly it seems road bike wheelsets are made for stiffness and CX/ gravel wheelsets may actually be better if they offer a
degree of vertical compliance?

But is such a wheelset in any way a bad idea for road riding?

Opinions is one thing, but is there any facts on this?

From inside, i heard a guy say both Ax and Enve wheels are to soft (he is strong sprinter and also ride track).
He like Lightweight best.
I have never used Lightweight, but i did find CCU a bit on the harsh side.

This question/ discussion concerns both road wheels and road/CX/gravel wheels.

So please, level this and share both opinions, ideas and facts (if you have such)

All inputs are appreciated guys!