The first one to say "I attack" should be the one to ACTUALLY go first.
I do see your point, and I've gamed that way before. The problems I have are:
1 - You may start to swing, even pre-emptively, but there's always someone out there quicker than you are.
I mean, what if you are normal Joe, and you suddenly haul off and swing, not knowing that you're about to fight a Navy SEAL?
Like a gunfight in the cowboy days, your enemy may be watching, looking for you to make a move, and once you do, you get it before he gets it.
Therefore, the random roll seems to suit the situation better. Give the "I attack" player a bonus on his nish.
2 - As the rule should be one-size-fits-all for monsters, NPCs, as well as PCs, it seems like it would not benefit the players at all if, everything they moved into a dark cavern, the baddies in there, sitting, waiting, in the dark, for the PCs to walk buy, would catch the PCs flat-footed a lot, without the PCs ever rolling dice.
"You walk into the grown-over cavern. You can hear a loud drop of water fall into a pool somewhere in the darkness. It happens every few seconds. As you bend down to strike the tinder box and light a torch, something big and dark separates from the shadows and attacks!"
And..the PCs can roll nish because the thing already attacked.
So, I think its a good idea to always roll nish, unless you're dealing with Surprise and Ambushes, but give modifiers on nish if needed.