I remember studies in China that showed the natural antibacterial properties of wood help with chopstick safety. I mean, trees don't get eaten alive by bacteria.

So far as fires and such: your local fire marshal would live to put a scare in you by burning up a polyurethane couch at a training facility. Wood naturally forms a char and likes to pyrolize slowly: it produces benzopyrenes and such but not with the deadly efficiency of a plastics fire. They have to add really nasty stuff to plastics to make them form a nice char.

Heavy timber generally takes longer to ignite, and longer to reach temperatures that can give rise to rapid fire events like flashover. It also tends to be more structurally sound under fire conditions than regular wood construction or plastics. It has a whole NFPA building type classification to itself (Type IV), and from a firefighting perspective can be safer to work in.

That said, because it lasts longer, it can reach higher temperatures when it does become fully involved (maybe that'll help with your first thought ;-) ). It's also nowhere near as fire-safe as Type I fire resistant structures made from concrete and protected steel, materials modern hospitals are traditionally constructed from.