Last time I played TOC I put it on the green on #10, way way WAY right of the hole (40 feet further and I would have aced #8's front pin position) I had over 150 feet to the #10 hole, and my caddie said that most people don't realize just how hard you have to hit a putt this long, and suggested chipping it with a 4 iron. I just couldn't bring myself to do that on those sacred greens, hit my putt 30 feet short, and ended up with a three putt for my kindness.
A lofted pitch may be an option from the Valley of Sin, but how many of us could bring ourselves to do it? If nothing else I'd be worried about trying to avoid digging up the turf in front of R&A members who might be looking out the clubhouse window, and blading it over the fence and scattering the onlookers