Although you could probably train some of these issues out of him, if you're not going to take the time to do that (could take a lot of time), neutering does tend to "calm" certain dogs down. If you can't control him at the vet, and he doesn't trust you enough to clip his nails or give him a bath, how do you expect to control him if there is a female in heat around?
Most behavioral issues aren't solved with a simple clip, but male dogs do seem to be calmer when they don't have extra testosterone. They also tend to not be as dominant and don't try to take control of as many situations/other dogs.
This being said...I have an intact dog, I'm not planning on neutering, but I don't have any problem at the vet or giving baths/trimming nails. My vet was actually shocked during this year's annual check up to feel testicles on my boy as he was super calm and behaved. He said its very rare for him to run into a GSD that is intact that behaves as well as mine does. But that is all training as most of the people on this forum will tell you that they also have well behaved males.
CD RE TC HIC 7/10