Damage is applied immediately, and yeah, people can be taken out before they've even had a turn. Generally speaking, I let the narrative dictate which side should get to go first..
The problem I see with this is in the nature of the way rpgs are played.
Player: I move down the cave. I've got my sword out and my shield readied. I'm poised for anything.
GM: OK, deeper and deeper, down into the earth you go. You've got to duck roots and narrow spaces, move around rocks upon uneven ground. This is definitely a natural tunnel with lots of turns, zig-zags, and elevation increases/decreases. Most parts are wide enough for you to swing your sword, but there are areas where you've got so sqeeze through.
You are now several minutes into the tunnel, and it's getting quite dark.
Player: I'll stop, fasten my shield to my back, then light a torch, and move on ahead.
GM: OK, that done, you sqeeze through a narrow rock opening into a larger cavern. You can hear water in the distance, but the pool must be beyond the light your torch brings you.
Player: I'll move towards the water, torch held so that I can see best, sword ready to swing.
GM: Before you, there's movment. A shape is moving towards you. It's moving at a pretty good clip. It's short, whatever it is...wait! A giant spider just came into view at the edge of sight directly in front of you--it's charging!
See, the players are reactionary to what the GM says. With the GM typically "moving first", you might end up doing more damage to the PCs than the other way around. Since there's usually many more NPCs than PCs, this might be a problem with your system--the PCs having to endur all that before they typically get to move.