I suggested something similar recently.

I agree that an automated system would be preferable. By getting (temporarily) deactivated without fanfare, the actual trolls would be robbed of the attention and responses they crave, and the naive innocents will be more likely to believe they've actually done something wrong and should reconsider their behavior, instead of getting self-righteous and feeling maligned and aggrieved.

If you automate it people will just sockpuppet their way around it, and other such attacks.

What we have is working well. Let's not create a system that people will be encouraged to game.

I find the process [...] to be a very unpleasant experience. It introduces all sorts of negativity and it makes me uncomfortable

Not me. And anyway, it's not you in charge of this process, so you could try to ignore it to avoid the stress, if at all possible. (It may not be.)

A lot of negativity seems unavoidable whenever anyone comes around the community disagrees with, either as a troll (like the "immortal" guy), or just as someone pushing weird and likely wrong opinions. I'm not sure the "kicking" part itself is a big part of that, so I'm not sure your solution would help.

I'd support the addition of the rule to the About page not because I'd have expectations about anyone's behavior but because it is apparently Eliezer's policy to enforce such a rule, so we should probably state the rule explicitly somewhere that newcomers are likely to see it.

In a sizable portion of cases, yes. But then again, how many people have we asked to leave? Maybe 5 to 8, no more. On the other hand, presence of this rule may make the endgame shorter, as non-admin users would be able to appeal to it.