Mike, I'm not talking about Tour statistics. I'm talking about independent analytics studies that have quantified the difference in scoring between different players and groups of players. The idea that we all know a local guy who hits it as well as anyone on Tour is laughable in light of what that research has proven, and it hugely underrates how good the long game of a Tour pro has to be. I just got finished playing nine holes with a fantastic young amateur in my city. He's a college golfer who hit 3w-PW to our opening hole, a 470 yard par 5. He missed two greens by a combined 24 inches. You would probably cite him as one of those guys who "hits it as good as anyone on Tour." In reality, he's giving away least 4-5 shots a round against an average pro when you compare their long games, and probably more. He's also giving away a couple shots in the short game and on the green, but the biggest gap is from outside 100 yards, not inside.
Considering that Tiger's most famous shot ever is a chip, I'm not sure your premise that we underrate the short game holds. I'm also not convinced that Phil's short game deserves more publicity than it gets. I think we probably properly rate the short game's importance, and maybe even overrate it slightly. But we also attribute things to short game performance that actually have more to do with the long game, which is one of the real misconceptions that modern analytics have proven when it comes to golf.
Case in point: the amateur I played with 3-putted that opening hole after hitting the green in two. Most people would say that he messed up with the putter after hitting two great shots. In reality, his second shot was a pretty big miss compared to what a pro would expect, and also left him in a terrible position considering the day's pin position despite being on the green. It was literally impossible to get his first putt inside 5 feet, and even Tour players would average over two putts from that spot (before bitching about how unfair the day's hole location was). But, of course, a Tour quality player would rarely hit a wedge 50 feet right of that hole, especially with today's course setup.