When I first got into sheep I was advised by an old farmer to trim routinely, then about 10 years ago I read an article in a magazine that said it was a bad thing to do so I stopped. I subsequently got less foot problems. I used to get a lot of foot rot and scald but now I don't. I put this down to routine footbathing in Zinc Sulphate.
As for overgrown feet, I think its a cause and effect thing. You see a sheep limping with over grown feet and its easy to assume that she is limping because her feet are overgrown. It is more likely she is limping because she has an infection that has also caused her feet to overgrow.