I had a zombie villager in a cave that was 'persistent' so I went up to the surface and built him a house so I could cure him. Built the roof out of brick deepslate stairs. Dug a hole and made a bubble elevator up for him. Had him go up and when I came up out of the mine, the only thing left of him was what he was holding. Following night, had a zombie follow me into the house and blocked him in. Slept close by and came back and he was on fire. Just built a quick house in creative using oak stairs and all zombies that I spawned in catch fire.

So using just stairs in a roof doesn't protect zombies or zombie villagers for burning to death.