Which part are you talking about? The entire thing?
Vsync sucks, yes. Creates a delay. Screen tearing also sucks, but less than giving yourself lag
FPS makes a difference for aim in TF2. I can feel the difference between 50 and 60 fps (I play on a 5 year old laptop so I often go back and forth between those 2 numbers)
I've only used 144Hz once (about 6 months ago during SweLAN) but did not notice any difference in airstrafing. Aiming on scout never felt so easy though. It even felt so responsive I had a hard time adjusting to it
I've also never seen anyone in TF2 mention that higher FPS affects airstrafing. You can test this easily by going on a jump server where you get double the fps as you would in a pub