Just to let all you wonderfull people know... this is still a problem march 25th 2023. Almost two years now.
Just adding my latest to the line to show this is still a problem. I cured 7 zombie villagers that spawned naturally (in a darkroom mobspawner). I got the zombie villagers out of the killing chamber. Trapped them in boats and cured them. 2 now have jobs with regular trades. March 11th... 2023.
I am having the same issue. As an example I uploaded a small video of two frozen Weapon Smiths. All the other villagers are moving, path-finding, working, etc. These two do absolutely nothing. Hope this can help. The villagers are non-cured villagers as you can see at the end by the prizes.
When playing on a 1.16.5 spigot server we're still collecting trader llama's... Maybe it's the server...
Can confirm that this is still an issue for 1.19.83: Campfires with a trapdoor above them do not passify bees.