It's very hard to achieve success that way, if I may rephrase. And despite Leicester's success post Ranieri (1 FA Cup), Tottenham made it to a CL final. But for a harsh penalty... who knows? Levy has placed his club in positions to challenge for major trophies across multiple seasons.
For every Leicester, there are hundreds of clubs that have sold their star players and promptly tumbled down the table. And for a club like Tottenham, it would be nearly impossible to replace a transcendental player like Kane, in terms of individual quality. Even if it's used to strengthen the squad, you're only potentially raising the bottom level, and losing an x-factor that makes the difference at the higher levels.
It's no surprise that a thread like this exists on a Man United site. "How dare they not sell their best player to us for a moderate price that will allow us to win the league". For anyone else, the last thing you do is let Kane leave unless a club is willing to pay an exorbitant amount of money.
