Nope. Just that police are not liable for failing to prevent crime.

If you are not liable for failing to do some thing then by definition you are not responsible for doing that thing.

No. I cannot be reasonably sued for blowing up my company's software systems for a failure on my part as an employee. It doesn't mean I am not responsible for keeping them up and running.

You can fire me. You cannot successfully sue me for the costs of my failure.

The fact that a police department technically has the option to fire a police officer for not acting to prevent crime (but the public has no recourse if the department does not do this) is hardly what I would consider to be genuine responsibility on the part of police to prevent crime.

How are those different in practice?

(Genuine question, no snark intended)

If I blow up a production system through an error, my employer can fire me. They generally cannot sue me for the costs of their losses.

There can still be consequences, just not compensation for losses.

You realize that the court case in question was about the police refusing to deal with a crime in progress, correct? If the police cannot be held accountable for their job, then what exactly is their role?

They can be held accountable through the democratic process and fired. They cannot be sued.

Exactly what democratic process are you talking about? We don't elect our cops, they're usually part of a strong union that prevents them from being fired and as you mentioned they cannot be sued.

So...how exactly do you expect them to be held accountable? These court cases were examples of the 'democratic process' and the court ruled that the cops have no duty to help you.