Fatigue is designed to break help LOS so why isn't it being expanded on instead?
Firstly, fatigue is a great mechanic for base kit Nurse. You lose LOS of a survivor, slowed and have obstructed vison. This should be expanded on instead of adding another mechanic.
Making it so she has 1 more second of fatigue would be a good nerf. 3.5 seconds of not being able to see a survivor and moving at a slower move speed is enough time for a survivor to figure out what to do. This is good for survivors who try to juke behind walls, not survivors who are W gamers. Actively trying to juke a Nurse should be rewarded not running in straight line.
Increasing the screen obstruction during fatigue could also help survivors break LOS. Good Nurses are looking at the top of their screens during fatigue to try to look for scratch marks. Maybe adding even more darkness around the edges of the screen could help.
Making it so you can't move after hitting/missing a blink attack could be a huge nerf too. Old Nurse actually had this in her hit before they made it so you could choose where you wanted to blink. Nurse still moves about 3m during fatigue on a successful blink hit. Not being able to move during fatigue would give the survivor 3m more of distance. It would even help more on missed hits where not only do they make distance becuase of the swing but if Nurse stopped moving, they could make even more.
Lastly you could reduce sounds during fatigue. Making it harder to hear during fatigue would make it much harder to track where a survivor went. Doing this would also add some more incentive to run her new addon that increases sound of pain after a hit and her perk Stridor.
All in all, adding a cool down is not the way. Expanding on her current mechanic of fatigue is a much better way to nerf Nurse. If Nurse is released with the current changes on the PTB, the games life will be cut short. Nothing stops the devs from doing the same to spirit and then billy. Then there is no one left to play as in high ranks for killer.
And after that there will soon be no more killers playing the game.
TL;DR Fatigue should be the thing the Devs focus on to balance Nurse. During fatigue you are forced to look at the ground, you have an obsucured screen and move slower. This is the main mechanic to help a Survivor to break LOS and try to lose the Nurse. This should be expanded on in ways that make finding a Survivor after fatigue harder but doesn't make playing Nurse unfun to play as. Deciding to add a cool down makes it seem like the Devs are just trying to hit Nurse in a way to please survivors in the short term and will only lead to the game dying in the long term.