You know those fake rocks that people hide keys in? How about instead of keys spawning in a fixed spot, we have a fake rock on the street that once people find it, they can push a button ,like the subway, and they get a key for the locked door. No respawn time needed. The search for the key could be fun.
Or have no key at all. Push the button and you have X number of seconds to get to the door, Indiana Jones style.