The problem you describe is real, but this program is a net positive (even in terms of the problem you're concerned about). Cops escalate mental health related scenes, which leads to people getting arrested and then put in a hold (which often gets extended).

If a social worker is able to resolve the situation without getting the cops involved, a cop isn't going to get personally offended that someone in crisis isn't "complying" and feel the need to punish them.