If you can’t get any live ones to service your city, you can hire some Dead Milkmen.
Taking care of the greenery at your municipal ballpark…park…ark, it’s
The Outfield…field…ield.
I assume we’ll get our news from a collection of Talking Heads.
To run your public libraries: The Librarians.
Public transit still needs some more work. Maybe you could scramble together a bus company by combining Bus Stop and Busdriver.
In the early 90’s I drummed in a band called Mexican Power Authority, the name adapted from a now-decommissioned entity called the Mexican Power and Light Authority.
Government Issue
favourite G.I. tune - “Hole in the Scene” - govt issue hole in the scene.wmv - YouTube
Need a house built? Hire The Carpenters.
Pet shop boys could be animal; control … and if ya want a sinister sounding name New order for when you conquer the world
Oh and Bad religion to run the churches 
And The Smiths to take care of your metalworking needs.
And, since they need a place to store equipment and stay while on duty but not active, they can occupy the 80s hair band Firehouse.
They would also need a fiREHOSE.
Which the OP mentioned…
Ambulance LTD
Cat Power (a power plant, right?)
Elf Power
Jets to Brazil
Radio 4
The Radio Dept.
The Submarines
And these guys could serve as some sort of temp agency in case an employee of one of the aforementioned public service departments calls in sick.
Manhattan Transfer?
Sounds like a junction on the subway.
And if those dudes couldn’t make it (;)), call these folks:
And if they bail, holler at:
I found some nurses.
And then there are these guys Public Service Broadcasting (band) - Wikipedia whose name is really appropriate for this thread
I especially like this track about the Apollo 11 moon landing - Public Service Broadcasting - Go! - YouTube
Depending on your personal proclivities, The Butthole Surfers.
No city runs without enough Bread to pay the bills.
Every town needs a GHOST
(not a public service, I know…just having fun)