Lineker and Rio Ferdinand were talking about this after the Madrid game - specifically, they briefly discussed why Kane was taken off after 75-odd minutes, and Lineker asked if it might have been because of his recent injury.
Rio basically said that the sports scientists are now pretty advanced in terms of their predictive statistical models and proactive fitness management - so much so that they can reasonably predict the amount of minutes a player can play in any given game without risking an injury. Thus, Poch taking Kane off after 75 minutes would have been because the sports scientists and physios were telling him that he'd hit the maximum safe time he could play for.
Thus, I don't think Kane will be anywhere near as badly handled as, say, Wheelchair was. Wheelchair was played in game after game after barely breaking into the team, over and over again for the full ninety minutes - it was no surprise that he broke down so irrecoverably after being burnt out like that so early in his career. But sports science has advanced enough in the six-odd years since that time to make such a thing happening again at a top club fairly unlikely. Players' fitness levels are closely monitored (down to the use of lasers, drones and cameras tracking the number of individual sprints and jogs in any given game/training session) and red lines are set on their involvement if it risks stress or fatigue-related injuries.
I think Kane's recent spate of injuries are just bad luck, really. Poch does manage his players reasonably well in terms of fitness - he has to, because of the grim work he puts them through in training. Look at his ginger approach to using Dembele - Mousa never finishes games anymore because Poch hauls him off whenever (presumably) the fitness people tell him that Mousa's race is run in any given game. I think that's down to our improved use of sports science, which is a trend across the PL, really.