I think each course has it's ideal rough height, but I like rough that is rough and not uniform. It should be somewhere in the 3-4" range, but it should not be uniformly lush. Some areas might be thick and nasty requiring a hack out while others might have much thinner grass allowing you to hit whatever club you like.
I have run into the same rough situation at two courses I played regularly in the past, and I wonder if it happens elsewhere. Each course had fairway, 5-15 yards of rough, and then long fescue. Both courses cut the rough to around 1". Both courses had issues of people looking for and losing balls in the fescue. People would look forever to find balls, especially after they lost a couple.
I suggested that they should cut the rough to 2-2.5", and was told I was crazy and just wanted to make it tougher since I was a low handicap. That wasn't the case at all, and my real reasoning was pretty simple. From my experience, the overwhelming majority of balls that lower handicappers hit into the fescue flew in or went in on one bounce. A large amount of the balls that higher handicappers hit into the fescue rolled into it because the rough was so short it didn't slow them down. A little bit more rough, but not so much to really make it too difficult, would help keep more of these balls in the rough, would speed up pace, and cut down on lost balls.
Only had one person ever agreed with me, the super. He couldn't do anything about it because the owner wouldn't let him.