It would not seem to be a part of the Federation's core philosophy to have a computer make the judgment about ending intelligent life. The computer would figure angles, speed, power requirements, but a sapient being would be required to make the ethical decision to destroy and kill.
So there is always going to be a living being's finger on the button. It might not be a actual firing button, but something labeled 'enable' or 'weapons release'.
In Errand of Mercy, the Enterprise was in a war zone, it's deflectors in that particular case may have been set to automatic, which wouldn't have alway been the case.