Is the whole party subjected to group consensus for all their actions? Does the rest of the group tell the paladin his Smiting is spoiling their fun? Or the warlock to stop using Eldritch Blast so much? Or when the fighter should Action Surge? And so on ad infinitum?
It is my humble opinion players should worry about their own fun. Why are people trying to step on someone else's enjoyment? What exactly is it about this ability that is supposedly ruining other people's fun? Maybe a little more introspection might help get to the root of the real problem.
Those abilities you list are by itself limited resources. I just see at will not necessarily as completely unexhausting. My push up example was not really serious.
But I can also scream loudly at will, but not for hours without rest. I would just explain that to the player and I believe honestly that no player would object.
I would also tell the warlock he can't fire eldritch blasts for 8 hours straight as I would tell the fighter he can't swing his axe for 8 hours straight. My reality check sensor would just ping.
I would not limit the use of shadow step to scout ahead for a few minutes. Let him repeat the jump 100 times without rest would be no problem. But when the shadow monk gets back, he is a bit exhausted (not the game effect).
Actually there is a precedent in the DM guide:
While dashing is at will, chase rules put a hard limit on the number of times you can dash in a row. After a certain number of dashes you need to do increasingly difficult constitution checks that make you exhausted (game effect) until you take a short rest. This rule btw limits the use of cunning action dash to just a reasonable head start. So extending chase rules to shadow jumps seems logical to me if it serves a better story.
BTW I have a shadow monk in my game who uses shadow step really well and often and I don't feel the need to put any limits on him. He does not jump around for the lolz.
And to the late post: If a single ability limits the creativity of the DM to have the party enjoy the story, the ability is indeed an offender. Putting a limit on that ability because it is to strong in that regard is better than not to play the story at all or in a forced way or to ban the whole class just for an ability that is not abusive of used in a reasonable fashion.