There was ping limit in the past and it didn't work. Most ppl only starts lagging when they interact with others.
Also melee range doesn't work like this. The game is build around "favor the shooter" mechanic (for both melee and guns) so this mean if someone hits you on their screen the game will register it as a hit even if it is not yet displayed on yours. This is why it looks like they hits you from far away.
Also idk how exactly random pattern would help against lag. It just increases the luck factor instead of skill.
However there are probably ways to reduce or make the lag less annoying but it will require rewriting the netcode.