I think that this would be not enjoyable. In multiplayer FPS, it would be enough to reach high hitrate. For example, players' hitrates are rarely higher than 10% (only in special cases). And it is hard for human to do better, because all players are constantly moving and players do not have such level of agility. However, I believe that AI could do much better. And AI reaching something like 80% hitrate would cause players to think that they are facing a cheater.
In single player environment things are even more complicated. Usually AI has massive advantage there (multiple controlled entities) and to be fun it has to be a bit dumb. Of course it cannot just stand in the middle but rather try to trick player into thinking that it is aware of an enemy nearby. Looking clever but stupid inside.
Yes, the trick could be choosing the target to optimize. I once had an online chess adversary that seemed strong but who appeared to be losing to me in complications, I even briefly considered an idea he was doing it on purpose to gift some entertainment and fun to his opponents. An AI targeted to do something creative and challenging and at the same time not trying to abuse its obvious advantages could be fun to play against.
You've hit upon the fundamental difficulty in game ai design. It's trivial to make an AI execute strategies perfectly (in most games). The trick (and the significant difficulty) lies in making it not perfect, but in a way that is humanlike, or at least makes sense.
If a solution to make AIs function at human levels, for example a built-in delay between seeing a player and say, shooting at them, becomes noticable, it cheapens the experience for the player significantly.
In single player environment things are even more complicated. Usually AI has massive advantage there (multiple controlled entities) and to be fun it has to be a bit dumb. Of course it cannot just stand in the middle but rather try to trick player into thinking that it is aware of an enemy nearby. Looking clever but stupid inside.