I built randuins on Anivia last night (try it, it's fun) and was chasing someone through the blue side raptor bush and forgot mid hadn't cleared the towers so I took like 8 or 9 turret shots from two turrets (cause Anivia is slow as fuck) while being hit by who ever I was chasing and a few of his friends and then I was like oh shit oh shit oh shit but I didn't die. I just kept on keeping on and I threw up walls and Q's and laughed my ass back to base (cause no way was I backing where there weren't any wards).
But honestly I think what would fix the system, or at least bring it back to season 2-4 norms, would be to have the first shot do flat physical damage like it does, the 2nd shot to do flat physical damage + magic damage. And then the 3rd shot to do %hp in physical and magic damage all while ramping up with the 5th shot just simply being an execute. If you take 5 shots you die.
That way an Ohmwrecker actually gets useful and rotating turret aggro becomes a thing again. Tower dives can still happen, but they have to be done properly instead of any kid with a snickers bar being able to pull it off.
EDIT: I didn't have any armor items built at the time. Just resolve tree conditioning and how ever much HP I got from Overgrowth. And it was 4 turret shots and a GP barrel (might as well have been 5)