My objection to them isn't the concept itself, it it is how repetitive it is on many courses. I've played some where every par 3 is a drop shot (after a long walk/ride up a hill from a previous green - wouldn't want to make people actually
play uphill after all!
I do prefer seeing something a bit original in the concept. My favorite course around here as a hole that 185 from the back, with probably a 50-60 foot drop (I'm really bad at guessing these things) but what makes it fun is that it plays with the prevailing wind and the green runs away from you (and the landing area in front of the green has a very steep down and to the right cant to it, so if you want to bounce on you better aim left and risk getting caught up in a little stand of trees if you veer too far left. The green is about 35 yards deep but while it is probably 50 feet wide in the front there's a second level in the back third that's maybe 30 feet wide. That is one heck of a difficult pin position to get close to, and there are 10-15 foot fall offs on the left, right and back surrounding that back part of the green so if you go for it you better hit it.
The combination of being with the wind and having the green and approach run away with you make it a difficult hole, but it is also reportedly the hole aced more than any other in the county (because the chances are better the more the ball rolls, a typical drop shot to a typical green has very little roll) When the wind turns around it is quite an intimidating shot to that green that looks so far away when you know the wind is going to rip your ball a new one with even the slightest mishit!