I agree - and here is where things start getting indirectly complicated/irrealistic:
1) e.g. the ambulance or the garbage truck get deployed from the opposite part of the map and then they get into traffic and they needs ages until they reache the target location, which is when my citizen is already because of "natural" causes or was choked to death by garbage.
2) I honestly don't understand how living just next to a hospital should increase the property value. "Nearby", yes. "Next-to-it" no (noise & lights & people in weird situations targeting the hospital walking by all night long? Definitely not an area where I'd like to live, hehe...).
The "too close is bad" is done by noise pollution. I think hospitals do not emit noise in Skylines, but the cars going to and from do, and other buildings have that built in, especially monuments, malls and metro stations.
People who live close enough to services get an additional happiness bonus for living close to the service on top of getting their needs fulfilled. The service still operates citywide, and people will still get all the benefits of having that service no matter where they live, but living close to one gets them an additional bonus.
There is also a traffic flow element here: people who live past a certain distance from the building have to deal with longer than expected travel times, so their ability to make full use of the service starts to degrade outside of the green. They're still covered by it, but it's not as efficient.