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.
Well shields and deflectors are defensive measures anyway, and it'd probably make sense to keep them on automatic for dealing with anything that gets past the nav-deflector or just some random bit of this or that junk that's hurtling towards the ship. And with cloaked warship running about, seconds count; so, again, common sense says keep the deflectors on auto and let them pop on whenever something shows up--you can always override and close them down if the object is a friendly.