Similar to what Sean asked: how would Oakmont play with no rough at all, except maybe in those ditch/hazards? Would the scores have been a lot lower? Would the course still challenge the world's best players?
Every player would have hit driver on every hole, and there would have been no penalty for being wildly offline. You really don't think the winner would have been double digits under par if there was no rough at all?
I disagree with Doug on this point entirely.
Look at The Masters, pre-2nd cut - they didn't always finish double digits under par, and Oakmont is one of the few places that has green complexes every bit as difficult as Augusta. The bunkering at Oakmont is certainly more penal, and in June it is firm and fast to the extreme. If they chose not to have rough, they could make it even firmer to compensate. This year was only brutally firm on one day, Friday.
Look at the results from the middle of the fairway at this year's Open. I don't know that they compiled anything anywhere, but when they would flash that graphic up with the little balls out in the landing areas, there were always a good percentage of fairway shots that ended up as bogeys or worse.
You wouldn't see the hack-out penalty, of course, but approaching those green complexes from the wrong side is absolutely a penalty.