It doesn't. It would be a great personal achievement but what is it all for if it doesn't contribute towards something bigger?
Kane has spoken previously about wanting to push himself to the best levels possible. If he scores as many goals as he has and ends his career without a trophy, that would be a huge failure for a player of his ability. If Kane has any ambition, he should be doing everything in his power to get out of Spurs. He holds all the cards now and has spent long enough dicking around in teams that can't match his quality to waste more time there. Renewing with Spurs would be consigning himself to a career of unfulfilled promise.
I’m inclined to agree with @Mcking personally. Being the outright PL record scorer is a far bigger deal than being one of many many PL winners I feel. Having come this far and this close to the record, I imagine protecting that takes a bigger priority than anything else now.