I understand why the Yankees may not have been willing to go to 10 years on a contract with Cano. We all know what a debacle the A-Rod contract has been and that's a lesson worth learning. That said, Cano has been one of the best players in baseball at a time when there was a fairly strong PED testing policy in the sport, and so some of the issues that have arisen with A-Rod (both in terms of injuries—which may very well be linked to his steroid use—and in terms of off the field and suspension issues) do not apply to Cano.
The Hamilton and Pujols deals are also cautionary tales, but those deals looked bad in year one, and so they seem more like bad bets in toto not bad deals because of diminishing returns in the back end of the contract. Unless you think Cano will forget how to hit next year, those contracts aren't clearly lessons in this case either.
That said, the Yanks did not want to go 10 years. Fine. But part of the Yankees's pitch was that playing in New York provided Cano with two things that no other location could provide. First, Cano would have the chance to become a legendary Yankee, maybe even the first Dominican-born player to be enshrined in Monument Park. Second, if Cano is serious about extending his brand beyond baseball, then New York was the place to do it, as it offered more advertising opportunities.
The second claim is complete nonsense. Like it or not, a Kevin Durant has a far bigger national profile than anybody in baseball right now, and he plays in Oklahoma. Playing in New York alone won't make Cano a national figure. Hanging out with Rihanna in the Philippines will. Being a baseball ambassador abroad, as Cano has been the last few years, will. Frankly, being the attraction for a major American sports franchise, the way he will be in Seattle, will do more to make Cano a brand than playing in New York. Remember when Ichiro toiled in obscurity in Seattle? No, because he was the face of the franchise despite not even speaking much English.
Now the first claim is the one that really irks me. You can't say to someone that there is value in being a Yankee for life when you're not willing to give him a contract that extends through his baseball career. Whether he'll be the same player or not, Cano will probably still be playing baseball 8 years from now. Which means that being a Yankee for life is only possible if the Yankees would still commit to him 8 years from now, which, based on how they are treating him now, is hardly a lock.
Derek Jeter was under contract, coming off a completely lost year in which he suffered two ankle breaks, and got a raise for no reason that increased his share of the Yankees payroll for luxury tax purposes, a payroll the Yankees are supposedly so concerned with decreasing. That's how you treat a life-long Yankee. The Yankees's pitch to Cano seems to have been: "You could be a life long Yankee! Just not with us."
His agents must have known this, and if Cano didn't, his agents informed him. That, more than anything about the contract, is why Cano left.