Because he's a good goaltender, but he's not elite. As Henchy pointed out, the number of games he started this season (a truncated season, mind you) was a career high. He's never had this sort of workload before. And the sample size of his playoff performance is mostly good, but still not a huge amount of games.
I don't think he's done nearly enough to "prove" that he can win it all. Not yet. He's certainly done more than enough to earn the right to prove himself, yes, but he has not yet allayed all those concerns. There are still some flaws in his game that other, elite goaltenders don't necessarily have. His rebound control is average at best, and he still struggles a bit to track the puck through traffic. He's also a guy who relies a little more on athleticism as opposed to technique and raw talent. That's not to say he can't win it all--certainly if he's going to, it's going to be with a team like this that is elite offensively, defensively, and controls the puck well in most situations.
The Avs have done a brilliant job building a defensive system that works perfectly with their starting goaltender, Bednar even alluded to Grubauer knowing for the most part when and where defensive breakdowns were going to happen, and being prepared for them.
Far worse goaltenders have won it all (Niemi) so it's not the biggest concern, but of course it's a concern nonetheless.