Plenty of imageboards have that feature. It doesn't tend to lead to higher quality content or a better community, though, it just leads to sockpuppet accounts, shitposting (because no one has any reason to invest themselves beyond the most superficial level) and mods with Napoleon complexes.

Do you think part of the "mods with Nepolean complexes" often happen because they are not paid ?

I think mods need to get reviewed and logs looked at as to why they deleted accounts etc. To me a mod deleting things that shouldnt be is a rogue employee. Personally I am part of some very heavily moderated forums and I really enjoy them. I find people invest because they appreciate it being looked after and not a childish troll fest that muddles finding good posts.

I think it's less the lack of pay as a lack of maturity, although getting paid might help them take their jobs a bit more seriously (assuming there's enough money to make that worthwhile.) A lot of fault lies with the administrators or whomever selects the moderators, who themselves may not be willing or able to act impartially or reasonably.

A lack of transparency in the moderation process can protect moderators from the social consequences of. Having known moderator accounts (not necessarily linked to user accounts) and a public mod log might make it more difficult for moderators to feel their position puts them outside the community.

And I think reversibility is important as well - nothing a moderator does should be destructive, as far as the database is concerned. At best, they should be able to flag posts and users for review later. I would even go so far as to suggest that mod actions which aren't approved get automatically reversed after a certain amount of time.

That exists in quite a few forum scripts. XenForo has a one click spam cleaner, which deletes all of a member's posts and topics, bans the account, checks their IP and mails them a message you type in about the ban (if you want to send one).

Quite a few others have similar solutions, sometimes as add ons.

And what do we do when the moderator uses that button to ban someone purely for his or her opinions being on the wrong side of the political spectrum, or unpalatable to the moderator?

Thats something that should be covered with the moderators beforehand as to what is to be banned etc. I personally would remove the moderator just like any other bad employee. Also why I think its a good policy to pay them and not just have people doing it for free.