No, police should instead be trained to respond in non-violent situations in order to mitigate police issues

Agreed. The main counter-argument with this is that cops get paid highly and it wastes their time. If you consider those social workers are paid around 15k less per year than cops, and if this was implemented, cops would be paid 15k higher a year for their additional abilities to control violent mentally ill patients better and considering that social workers would have to call the cops anyways in that situation, you are actually saving money!