Priming on or off the press seems to be safe.
Improperly using a primer tube and not inspecting it is unsafe.
The main thing is once you get a primer to the primer punch, it is not going to set off a bunch of other primers (located at least 6" away) and will, unless someone gets creative, do no more than get crushed if the loader isn't careful. Any danger, at the primer punch location, has nothing to do with press or bench unit or hand primer and everything to do with forcing things.
Rule of Reloading: Don't force anything. Fix the problem.