From what I can tell looking around on Steam forums, this isn't the range of the service. There are two things going on:

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.

> 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...

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...).

To 1, yes, that happens. Makes it impossible to have cities where not every area is connected by roads. It's also why it is so important in this game to not have traffic jams. There is a recent mod for this however: https://steamcommunity.com/sharedfiles/filedetails/?id=16808..., Most Effective Traffic Manager. It changes how the routing works and tries to combat exactly this. Though I could not just add it to my current rather large city, it dies with null pointer exceptions. It might work better now that it got some patches or when starting from scratch.

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.

What about the paragraph before that?

> the service needs to be accessible, so either citizens need to be able to get to the buildings in a timely fashion, or the buildings need to be able to send their vehicles out to various parts of town in a timely fashion. If traffic flow gets bad enough that this fails to happen, citizens get upset. All you need to have effective public services is enough capacity + traffic flow for your citizens to make use of them.