How can I lose the drunkard trait?

It's hard to prove a negative, but as of version 1.1 it doesn't seem so.

I did a text search on the game's script files which describe all the interactions, events, decisions etc. in the game (Crusader Kings IIIgamecommon) for the string remove_trait = drunkard and received 0 results. I then did a search just for drunkard to see if there is maybe a different syntax for removing a trait. I found a lot of results which check for that trait's existence or add it, but none which seem to remove it.

So apparently the one enemy you can not defeat in CKIII is alcohol.