The main problem I have with people chasing kills is when they're chasing kills they will obviously never catch.
If you are playing a melee character and you're trying to chase down Ashe by yourself, stop it. Just stop. It's not going to happen unless she is a complete idiot, and even then it's unlikely. This is a character designed to run away from you. You are wasting your time and likely going to get yourself killed. Likewise: Nidalee, Singed, Rammus (Wait why are you chasing tanks anyway? Cut it out.), and so on.
If they're chasing a priority target that they can actually catch and kill, I usually don't have a problem with it. It's unfortunate that that is so rarely the case.