Good monitor reviews include a test of the delay. 3 frames delay (<100 ms at 60hz) is absolutely atrocious and easily detected by players in games.
But of course, that's not the problem. It's ok that the phone doesn't unlock with out me noticing the delay. It just can't be so long that I start doubting whether it works.
Yes. You'd feel quite drunk even controlling the mouse pointer with 100ms lag. This was/is actually a problem with some LCDs (VA in particular) that cached a frame or two in order to "anticipate" future changes so that they could adjust the voltage and make the image transition faster.
This overdrive is probably also the cause of burn-in-effects that seems to be especially common in VA panels.
The question is could you tell the difference between your 144hz monitor and your 144hz monitor with the signal delayed 100ms.