Your idea has been set forth by a more than a few of the
deathmatch whores who
absolutely must be fragging at all times. Unfortunately, it has
two major flaws that ensure
the idea will never see the light of day.
1. Lag. Essentially, the server becomes two servers, as it is determining coordinates and actions for two completely separate games. While the deathmatch game could be integrated into the same map currently being played, and the server could just not send the information to those playing in the other game that is occurring in the game still being played by the living, this could prove to be much of a load for the server to handle. Granted, most servers could handle it, but many could not. The client suffers as the server suffers. I'm a 56K HPB, and it is tough going in the early part of a round in a large server when my connection simply cannot handle the information being sent by the twenty-some players in it. In the later parts of the round when most of the players are dead, I can play a hell of a lot better when my packet choke isn't hovering in the 50 range. If the server can't bear the brunt of the packet load, then I'm going to have lag issues just the same.
2. It destroys the magic of Counter-Strike. What makes this game special is that you get attached to your life, unlike an actual deathmatch game like Quake 3 where death is an afterthought to killing opponents. Most people probably wouldn't think about this fact, but would definitely see how less fun the game would be if it included constant respawning. Counter-Strike is set up to make surviving actually important, and that's something I think draws a lot of people to the game. Also, the death time allows for community to be built through the banter that goes on between living. Getting to know people in the game has been one of the things that makes the game that much more fun for me, as fragging a friend is a lot more satisfying than fragging Nameless Idiot #306.
Basically, if you want to be fragging at all times, go play Quake 3, or find some other game with realistic weapons and respawning. Action Half-Life, perhaps? Don't touch the beauty of Counter-Strike, because the flow of the game is flawless the way it is.