I don't think having 4x weaknesses changes the dynamics of pokemon holding Assault Vest over anything else. You are still aware that you're not gonna leave AV Tyranitar in on a Breloom just as you would never leave him in holding anything else.I also think an assaultvest user should not have a 4x weakness for a common attacking type cause it will be sniped with moves of that type.
But I do agree that the mon should have some form of natural boosting, since AV limits your set-up to just Power-Up-Punch.
But I've actually had a lot of success with AV Magnezone, with the analytic ability being your free life orb, Specs Analytic is still a better set, but becoming a 3HKO on special attackers is more life-saving than you think.
and AV T-tar is also just fun to use imo, knowing that even a Mega Gengar Focus Blast isn't gonna KO it is a beautiful thing. Give it power up punch for some offensive set-up and you'll be surprised how far it takes you.