No, they do have an obligation to protect the public in general. That's the point of police.
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.
> No, they do have an obligation to protect the public in general.
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?