The code for the AI and bots is already there... it's in the single player game.
Coding AI that can intelligently react to multiple
players, each doing something different is significantly more difficult that that which only reacts to one player. Especially so, if the AI has already been written with one player in mind.
In addition, scripting becomes a nightmare. Any segment in which a door closes behind you, a bridge falls down as you run across it, monsters spawn where you are not currently looking, the lights turn out when you enter a room etc must be taken out or drastically redone with much more robust code than is necessary with one player. Ammo/weapon/health distribution must be rethought (frequently each client is given a copy, but this is a hit against realism).
Plot and NPC interaction is also very tricky (though it can usually be ignored in most FPS...), as every player must remain informed of plot development, dialog and current objectives...
fairly simple in a game like Serious Sam... Players trapped behind doors receive a magical teleporter to bring them to the rest of the group and scripting generally doesn't get much more complicated than that. Plot is unimportant and AI is basic ("run at player and shoot") enough to make less it difficult to implement than in any game where the enemies are supposed to do anything interesting.