#2 Chance to lead by example
If Kane ever were to set foot in Madrid in a Los Merengues shirt, it'll mostly be so that he can come into the team and score goals. Plenty of goals.
Harry Kane can execute that task with a aplomb. Ideally, he would be brought in as a replacement for Karim Benzema in the No 9 role, with Ronaldo and Bale on either side of him. His primary duty would be to bang in the goals, given that this Real side is severely lacking that at the moment.
Kane would have the chance to lead the team by example, help raise their game and secure good results with his prodigious feats on the pitch, just as Ronaldo has been doing for so many years at Madrid.
Now with CR7's powers have seemingly begun to (understandably) wane, that mantle would be placed on Kane's shoulders, and he comes across as the sort of player who relishes the task of being a team's protagonist, which he probably will go on to be.
Even though he is the go-to man at Tottenham, the responsibility would be much higher at Real Madrid and it's difficult to not see him thrive in such a role, and who's to say that he cannot go on to brandish the captain's armband in due time?