2nd thought: The fire inspector just got interested. He wants to see your documentation - for that engineered wood meeting Hospital-level fire resistance standards at 30% oxygen.
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.
"Natural antibacterial properties" is not a regulatory certification. The hospital is regulated, and may also feel responsible for making sure that they can 100% sterilize surfaces - after those have been exposed to a wide variety of bacterial, and fungal, and viral human pathogens. Maybe add prions to that list.
My rhetorical fire marshal isn't the point. Fire behaves very differently when oxygen levels are elevated. Are you familiar with how wood fires behave at various % O2 levels? (I don't actually know that 30% O2 is the hospital fire safety standard. The standard my vary by state, or be higher in ICU's, or etc.)
EDIT: Bigger picture: Yes, using wood looks plausible. And it could help patient, staff, and visitor moods. But hospitals are not a "just try it, and see what goes wrong" use case.
Neither do I but I don’t think my natural antibacterial properties are sufficient for a hospital
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.