I don't know about NYC's new program, but Portland has been doing something like this for a couple years. They send out teams of a medic from the fire department and a counselor/social worker with specific training in deescalating acute mental health crisis.
There have been no incidents of these teams being attacked or injured.
This "under siege" mentality that the police have adopted as central dogma, which clearly has spread to you as well, is the problem.
I'd suggest reading the various interviews and comments from Patrick Skinner. He's been on a solo crusade for a more compassionate approach to beat policing for a few years now. He gets a lot more clout with police with it though, as he's ex CIA, so no one questions his machoness. The very core of his approach is "how would you solve this without a badge and gun?"
It's simple. It works. It's moral. It doesn't mean we abandon society to anarchy, it just means we stop seeing citizens and police as enemies of each other, where the default assumption is that a restraint and a gun are necessary to even have a conversation.