The police do however love opportunities to justify large expenditures and fancy equipment.
Many courts have upheld this principle:
BARILLARI v. MILWAUKEE http://www.leagle.com/decision/1995441194Wis2d247_1431
https://en.wikipedia.org/wiki/Warren_v._District_of_Columbia The Court explained that "[t]he duty to provide public services is owed to the public at large, and, absent a special relationship between the police and an individual, no specific legal duty exists."
What they don't have is financial liability for the death of every specific person they aren't smart/fast/legally empowered/well-funded enough to save, because that would be unreasonable.
I see your point but I think it's a pretty arbitrary one. Have a police force every been held legally accountable for failing to protect the public? The case law that the police have no particular obligation to protect individuals is well established.
What does it mean to have an obligation to protect the public when the public is made up of individuals and the police have no particular obligations to protect individuals?
Lots of things can result in bad shit--but we seem to be looking at the civic equivalent of rheumatoid arthritis.
If a fire department shows up without need nobody is put in prison, shot, assaulted, or has their dogs killed.
I discovered this isn't true, at least not in Lowell, MA (a bit north of Boston, MA). A few years ago I bought a 3-family rental property. There was a big blizzard that froze the badly insulated water pipes in the house, which resulted in the pipes bursting on the 3rd floor. That caused what amounted to a waterfall inside the 2nd and 1st floors.
When I arrived, the fire alarms were on. I was going to head down to the basement to turn off the water main but then I realized I had no idea where the water main was (I had just bought the house) and I figured that venturing into a dark basement full of water with live wires running everywhere probably wasn't the brightest idea.
So I called 911, explained the situation, and waited. They told me they'd "send someone". 20 minutes went by. The waterfall was still going. I called again. They told me they'd send someone. 10 minutes went back. I called a 3rd time and was told "they're busy clearing snow from fire hydrants around the city". I happen to be standing next to a light switch in the house and I happened to smell something that smelled like smoke. "But I smell smoke", I said to the dispatcher.
"Smoke?!", she replied. "We'll send someone immediately."
And within 3 minutes I had a dozen firefighters in the house.
Your anecdote seems to support the statement "the fire department has to respond to every fire alarm".
And I explained that to the dispatcher.