Our federal regulations require a harness that can lift a diver out of the water, which is covered by this harness c/w crotch strap. We use to have a separate harness but went away from it simoply because what we had now suited what the requirement was. One of the big points is like dittrimd stated about ditching gear and still being on a line. We do not train that way..., no diver we train ever deals with removing his/her equipment underwater. If it gets to that point, our safety diver is present in the water and has cutters for the harness/webbing and they cut the diver out. That way the first line (which may also be an issue if the diver is fouled enough to warrant ditching gear) is clear as well and the rescue diver line is still in place.
We do some searches with hand holds only, such as hull and pier searches, but we treat those as search lines, not life lines. From our point of view a diver holding a line is the same as a free swimming diver and is treated as such as far as protocols are concerned. (dive buddies, floats, etc)