Shouldn't someone with a history like that be prevented from running for the most powerful position in a community?
I would think no, they should not. I have seen people make the most surprising changes over time. Don't doubt the ability of people to actually get better. That someone has been banned once is by no means reason (in my mind) to prevent them from ever being a mod.
Or, at the very least, shouldn't his election profile show the number of times that his user account has been banned on any SE site very clearly and prominently?
Now this I would agree with. While having been banned shouldn't immediately disqualify you, it's certainly a very significant point against you. It's important that this information be available to voters in my opinion. By nominating yourself you should be revoking your right to privacy (to at least some degree) around such situations. If you aren't comfortable with people knowing that you were banned, and at least some high level details of what happened, then you shouldn't be running to be a mod.
Such a user would need to be able to discuss what they did in order to demonstrate that they have changed since then and that such behavior is behind them; that they will be capable of acting responsibly going forward. If a user is able to do that after being banned, and the community accepts it, then that shouldn't need to prevent them from running at all.
Now, as to this specific case, it does seem that this behavior is not behind them at all, that they haven't changed, and that there is no way the community would support them; if they did, it also sounds like a case where the SE employees would put their foot down and reject them.