So this idea keeps coming up in this discussion.
It’s true, in the sense that you can’t sue the police for failing to protect you (in general).
But this is basically true of all public officials. You can’t sue the city for not maintaining your road adequately. You can’t sue the DMV for making you wait in line. You can’t sue a school (generally) for providing poor quality education. Etc. The reason for this is that these entities have “infinitely” deep pockets so if they had normal liability, in the end, the taxpayers would be making enormous payouts all the time. The recourse you have is not the court, but rather, the ballot box. If your schools aren’t good, you don’t get to sue, but you do get to vote for a new school board. If your police are not good, you can vote for a change through the city council. Etc.
So you can’t really say, “I can’t sue X for not doing his job, therefore it’s not X’s job” in this context. You do get to vote for change. You may feel that vote is powerless or useless, but that is your recourse, and police, and other public officials, do have a duty to do their jobs.
This does lead to some unsatisfying outcomes. In one horrendous case, a chimp in Connecticut caused horrific injuries to a woman, and she sued the state for allowing this dangerous chimp to be kept as a pet. The suit was dropped, even though it was obvious that the state had failed to do what it should have done in that case. They are immune. So yeah, it’s sometimes unsatisfying that the state has has immunity, but your recourse is through voting. And if the state did have liability, they would be sued for a billion dollars every day and they would collapse. So that’s how we have the system we have.