It’s not just a matter of not showing up. They can be ordered to stand down. That has happened a number of times.
I don’t want to say much here or get into legal minutiae, but I’m a lawyer and I’ve discussed this at length with both a sheriff of a highly populated county and a mid-size city police chief. I understand the law. I also understand that every rule has an exception and laws have to be considered in light of a specific set of facts. All that said, generally speaking, in a riot situation they have no duty to step in and defend you.
Again, I appreciate your insight and I understand your legal explanation. In your example, they could be told to stand down. In that case, one could argue that any responsibility has now been assumed by the higher authority ordering the stand down. Ultimately, they work for the public and the public can hold them accountable, via elections, or otherwise, and can fire irresponsible officials.
Some of my argument (and I am certainly not a lawyer) is probably semantic. Duty seems to have become a legal term, meaning if its your duty and you fail you can get sued, prosecuted, etc. Duty used to mean doing the right thing and we didn’t need laws to tell us what that was. And I guess that’s the second part of my argument (not with you, just my rant), that if police have no duty to protect, what are they but a tax collection tool. If firemen have no duty to put out fires, why have a fire dept. Etc, etc.
As I said earlier on, the world is on its head.