Thank you all for your thoughtful engagement on this topic. This is not a hill that I'm willing to die on, but I think it deserves some discussion and consideration. Let me briefly respond to a few points that have been raised.
Let me first clarify (in case it wasn't clear from my original post) that my recommendation would only apply to elite competitions. I'm certainly not recommending that the agronomy of our home courses be changed day-in day-out.
I was surprised to see so many people responding as if my proposal was an extreme one. I'm essentially just recommending that we play around with the mowing heights of the rough for professional and elite-amateur tournaments. Compared with redesigning courses, building new bunkers, or mandating new equipment, this is such a trivial, low-cost change. Maybe those other things are worth doing as well, but this is a very low-cost change that could be implemented unilaterally by tournament organizers on relatively short notice.
I'd also like to point out that my recommendation would introduce a new layer of strategy not currently present. Every tee shot will pose a new risk-reward tradeoff that wasn't there before. I think that would make elite golf more enjoyable to watch, and it would make the game less one-dimensional. (I also really like Jeff's idea for architects to give guidance about where the rough should be thickest in order to enhance strategy and highlight the architectural features of the holes.)
Great questions have been raised about the problem that we're trying to solve. In my view, there are two related problems. (1) High-level competitive golf has become too one-dimensional, meaning that players who can't carry the ball 300+ but are otherwise very skilled and talented can't compete. (2) We're often altering our classic courses for the worse just so they can host a four-day tournament once every 15 years. Even if you don't care about problem 1, everyone on this site should care about problem 2. And as long as problem 1 is around, problem 2 will be as well, so we should be looking for low-cost solutions to problem 1 that don't exacerbate problem 2.