I'm not so sure about injuries - Most of the time wasting injuries aren't treated. It's the player going down with cramp as soon as the ball is collected by their own keeper, or waiting till they've got a throw and sitting down.
You might hope that if you get the trainer on, then the ref doesn't add the full extra time, but the real killer is constantly breaking up momentum. The constant 20-30 second breaks when a player sits, but then waves away the ref, and just gets up slowly aren't there in the hope the ref only add on 15-20 seconds, they're done to give everyone a quick breather, to get back in position, and to mentally reset. The constant stop start also gives the attacking team time to think about the seconds slipping away, putting extra pressure on, rather than allowing them to build up momentum.