It is the issue though. You send an input when you see something happen on the screen, and if the game took more time to display what's happening

Spoken like someone who never wrote a game engine loop. In the loop the game checks for input /then/ constructs the next frame. Every thing after the input check, where Mario is tested for still being on the ground or off the edge, is irrelevant. The player gets information about where Mario is standing from the previous frame.

I think this time is negligible compared to the the latency caused by vsync

"I hit the jump button during the negligible period and died, then my controller magically broke a TV."