As Anthony knows, our Superintendant Gregg Stanley is one of the best in the country and can grow and mow grass with the best of them(to say nothing of his course building/renovation skills). He also has the skill and resources to keep them not only fast, but firm.
At one point our approaches were walk mowed .23 of an inch-putted beautifully.
We had numerous discussions about playability and his opinion was that it helped the average guy by allowing him to putt.
He also liked the aesthetic-which was very clean.
I shared my opinion of reduced options/skill lack with the extreme short cut and also shared that even though SHOULD putt they often didn't due to ignorance/inexperience or wanted to use their chipping/pitching skills more often-when they did they duffed it most of the time.
After experimenting he has settled on a higher cut for approaches(same as the fairways using same riding mower) to produce better contact and more options(no doubt the cut is lower than 99% of all approaches still)
he also mows them TOWARD the green which allows a slightly higher cut with more grass yet allows a forward bounce due to mowing direction.
edit:Of course he also does a lot of rolling -often instead of mowing-(see Anthony video below)-which allows more grass.
I believe he has changed his practices slightly since that video was shot-uses same method on approaches as fairways and mows/rolls toward green everywhere.
The members didn't even notice-they just think their skills improved.
This is not a solution for most clubs as it does require resources/equipment most don't have(but no more than the previous approach-maybe less), but it sure makes our course more fun to play-and is an example of using turf skill and experience to serve both the aesthetic, function and playability.