I can't possibly find a way to disagree with this post anymore. How many times have we seen interviews with ex pro's, managers, colleagues etc... who shout from the roof tops about how much of a model professional he is?! He is always referred to as an extraordinary trainer who leads by example and works incredibly hard.
What is the issue with him wanting to get back out on the pitch as soon as possible? We would all be complaining if he refused to make himself available for weeks because of the fear of becoming injured again. At the end of the day, Harry doesn't pick the team, the manager does and it is up to them if they want to play him.
To further support your point. He idolises Tom Brady, who is famed for his hard work off the field, so I can only guess Kane would try to emulate that.