Choice and Tryndamere's ultimate.

If he gets caught out during a split push and he knows he is going to die without killing anyone anyway, should he be allowed to just hold his ultimate? Shouldn't coordinating and outmaneuvering him on the map to kill him (perhaps even giving up a strategic resource like a tower or dragon) justify that at the very least he can't use his ultimate again until it comes off cooldown?

But it won't be on cooldown if he doesn't use it, which kind of invalidates the choice of fighting him instead of contesting another objective, because from a purely strategic point of view, in fighting Tryndamere you risk everything and gain nothing. He will just go straight back to doing what he was doing, with no temporary loss in overall power, because he didn't use his ultimate, which means it will take just as many people as last time to counter his split pushing, and he probably still won't ult if he thinks that it will create a window for your team to handle him with 1 champion rather than 3.

Shouldn't Tryndamere's ultimate be automatic then, so that it automatically activates it he would take what would otherwise be lethal damage? Wouldn't that offer more meaningful counterplay to his split push?