I think it is more psychological. The dog has a feeling it is restrained and is more likely to stay put.

They should ALWAYS have a safety release, like the cat safety collars or something like that.

And the dog should not be left.

Having said all that, the 2 times I've had Sugar to a groomers, they didn't use one on her; she is such a statue when she is getting a bath or being groomed, they didn't bother. And I've had no trouble working on her here at home (as a beginner, I take TIME getting little trims done, and she is fine!!!)