I'm just picturing a situation where it's the last 3 minutes of a crucial game, the team need to hang on or they're relegated. Someone goes down with an injury, it feels bad but they know if they go off they're not coming back on this game and they'd leave their team down to 10 men when their goal is already under siege, so they stay on, get a kick in a tackle and damage it even worst and miss half of the next season.
As annoying as the people rolling around on the floor are...if it comes down to putting up with them or risking injuries, I'm gonna have to plump for the former.
What about giving the referee discretion to keep a treated player off the pitch for up to 5 minutes. So if he genuinally thinks there was a problem, he can bring them straight back on, if he's not sure he leaves them a couple of minutes, if he knows the guy was just faking it he can go up to the full 5.
It has its own problems, just give refs another reason to be hated, but I'd prefer it to mandatory time.