To be honest, I think either way can work... On one hand: on my 'home' forum, numbers are barely ever used at all in a fight (other than prep counts) and I've been able to do several fun, clean fights there. On the other hand, I've also been on forums where everything is stat-based (e.g. 'my character has 20 speed, and can therefore run a 3 minute mile') and have still been able to do several fun, clean fights.
So really, I think people should just go with whatever system they prefer. The fact is that problems and arguments don't arise from a specific system, they arise from people being stubborn. From what I've seen, such people will start arguments no matter which system is used... Now, whether or not arguments are a normal part of RP fights or not is a whole different can of worms, but essentially using numbers or not using them won't help much if the people fighting are already the kind who don't get along smoothly.