The "he hasn't won (or hit) in the playoffs" thing only gets said about the very best players (and the ones who play on teams that make it to the playoffs often). Bagwell, Barry Bonds, lots of others (conversely Jeter was extremely productive). But it's all pretty much SSS/random.
But I agree that if the Nats win a ring this year that will absolutely be the national story. "They were better without the guy who was once viewed as the best player in baseball." By that logic it also justifies the fact that they low-balled him. Their GM looks smarter than ours, dumping Harper and focusing on pitching.
I'm not saying this is actually true, and of course the reasons the Nats lost in other years (or didn't make the playoffs at all) were myriad, and hardly just about Harper. But that's what being a star player is about. Most people don't remember 2010 and 2011 as years when the Phillies' elite pitching wasn't as good as the Giants and Cardinals pitching. They mostly blame Ryan Howard for striking out a lot.
As for Philadelphia, I think we can be bitter about the Nats winning a championship regardless. And we'll also be bitter if our $300 million player doesn't win one in his 20s regardless of what the Nats do.