Jon,
Should have mentioned that I had a long discussion with Lanny Wadkins on design a few times. Once, we discussed tiered greens, and he didn't think they should not be there, he just seemed to think they should be very limited, grudgingly upping his max to 4 greens per course, with variety, i.e., some side to side, not back to front. Even then, I have heard some players complain that from the higher side, you can de-green a chip or putt to the lower level, LOL.
But, even more than putting on a 2-3 tier green, Lanny mentioned that they might inflict a disproportionate penalty on the approach shot, i.e., coming up one foot short may make the difference between being 5 feet from the pin or kicking back 50 feet. He recognized that it happens on occasion, that a tier is necessary to take up grade on occasion, etc. But, he didn't want a tier designed into a green with his name on it unless he could defend it as necessary, i.e., definitely not on flat ground. And, as someone has also opined, a built up multi tier green on flat ground somehow stands out visually as bad or at least artificial.
Short version, what design feature is so good you want it all the time? None, really, and that is especially true for a design feature that might add to your own self inflicted penalty for a bad shot. Of course, a related question, especailly when redoing old, steep greens....what is worse, a constantly steep (i.e., 4% or more) downhill green, or one remodeled into two 2% areas, with a tier in between that might accelerate a putt off the front of the green just as much as the constance 4% would, maybe just not as often?
All design is a compromise, in some ways, picking options that lead to the least bad outcome, LOL.