Not entirely the same, but here in Canada (still common law), any housing covenants applied to a deed can be struck down if they are illegal. There were a bunch of houses with ancient unenforceable covenants like not selling homes to certain ethnic/religious groups and they were granted the right to no just ignore, but actually remove those causes from the deed. Transitively, I imagine any deeds for HOA rules and regulations that are illegal under the law could also be challenged under similar merits. I've got no examples of this though, so who knows.

That definitely seems like the easy case, sure.

I'd be extremely interested in cases of any modern HOA being successfully removed from a deed and thus rendered moot, ideally administratively without a massive legal battle.

You have to get all parties to agree to remove the restriction. I've heard of it happening.