One part of your idea I quite liked - police being able to use a "respond" command to show that the call has been received/something is being done.
You could build on that, so that once an officer picks up a 911, dispatch can automatically send a message on /c r stating that (Officer) X is investigating 911 from (citizen) Y. That way, for a small crime you don't end up with the whole police department at your doorstep, and at the same time indicates to cops whether a call has been responded to or not.
I sometimes do /me responds to 911 call when I get one, but this is not always that efficient, and why clog up the chat if it is busy?
P.S. JAMEZZZ, if someone has the tendency to misuse /c 911, police may be less keen on responding to them. I bet everyone's familiar with the "boy who cried wolf", right?

VCPD - the official police department - does try and get to every 911 that comes in. The only time when this doesn't happen is when all operatives are already involved in a situation, in the middle of a pursuit, for example.