What about a broken waterpipe? That's the most common emergency where a landlord or maintenance staff needs access to prevent building damage.

Who pays for the broken door?

If it is really an emergency (fire, heat failure, plumbing emergency, etc), not kicking down the door will cost far more than the $200 that a new door costs.

Apparently everyone decided I was proposing letting it all burn down. I was only wondering if, by letting the landlord have a key who could be used in an emergency, the tenants where reducing the risk of being on the hook for those extra $200. Of course the emergency must be dealt with.

Insurance company.

The apartment owner, or perhaps their insurance.