Quick silver sash now has a 1 second cooldown BUT using it damages you.

Read the whole OP before commenting. The QSS doesn't just damage you, it does other things to you that make you not want to spam it and provide reasons to champions like kayle or tryndamere to not use it during their damage immunity.

It deals 15% of your maximum health as true damage to yourself over 5 seconds and applies grievous wounds during that time and grants negative 15% tenacity. Different instances of the dot stack, cannot be removed by any means, and cannot reduce you to below 1 hit point.

Basically you can choose between being crowd controlled by a spell or taking damage to be freed. So if you snare a target hoping to chain cc and kill them then will be disappointed that they got away, but at least you can take comfort in the fact that the single CC spell forced them to lose 15% of their health and half of your healing for 5 seconds in order to survive, AND it makes them more vulnerable to any other CC for 5 seconds. Furthermore if you or your ally are able to CC them again before they can get out of danger, they will be again forced to use QSS or else be CC'd for longer (due to the negative tenacity).

It becomes a kind of thing where someone who just uses quick silver sash without respecting its cost in order to get out of sitations that they should have died in end up being forced to use it over and over (because of the ramping negative tenacity) and end up dying because of the self inflicted damage. That is intentional-- we wouldn't want someone to just ignore CC because they think they can spam QSS every time they get CC'd.

The point is to make it difficult to ruin someone's day with just a single CC spell without any backup, like being rooted by a single morg binding in a team fight so that you can't assist your team even if nobody on the enemy team follows up with damage. With this you can say "Ok i'm willing to make myself more vulnerable to future CC, take 15% of my health in damage, and reduce any future healing on myself by 50% for 5 entire seconds if I can just ACT NOW."

If you are forced to use it one time you take a total of 15% of your maximum health and suffer from 15% negative tenacity. If you are reckless after you use it one time and then have to use it a second time, you will have to lose 30% of your health and suffer from 30% negative tenacity.

And no it wouldn't be overpowered on tryndamere (or kayle) because of this:

If he has to use it a bunch of times in a row while he is ulting to make it so that he can shrug of CC, he would end up taking an enormous dot that would guarantee that he would remain at exactly 1 hit point for about 5 seconds even after his ultimate ends, and he would probably have upwards of 45% or 60% negative tenacity, so a 2 second stun on him just before his ult ends will last for roughly 3 seconds, and a 3 second binding will last for almost 5 seconds, ensuring that he will die after his ultimate ends if he chooses to spam QSS.