Why are you trying to find consistency in the worldbuilding for this, it's nonsense. Like, by all means enjoy it for whatever reasons, but logical and consistent lore and narrative is not one of those reasons.
The entire Human Behavioural Biology unit lectures at Stanford, by the brilliant Robert Sapolsky, are online and they will change the way you understand yourself and others:
It' goes into some fairly deep science but is still very accessible, Sapolsky is a brilliant educator. His book Behave is basically these lectures in book form, the audiobook of it is on Spotify.
He's not at all invulnerable, in the book they were about to throw down and the Witch King was pretty confident about his chances. Also Gandalf literally gets killed by the Balrog. And beaten and imprisoned by Saruman.
This is exactly what the previous comment is saying. Jackson changed stuff for the movies to cater to mainstream movie audience expectations, at the cost of the worldbuilding and lore.
That's not the correct way to assess the issue.