Is it time we brought in another type of official to deal with these cases? - this is a good question and I have no doubt that your motives are also good.
But how would that work out in practice?
Cops patrol the streets, focussing on pedestrians, and traffic cops focus on people driving their vehicles.
It's typically impossible to know if citizens are suicidal or homicidal. I guess if you had a case of a man on a bridge threatening to jump off then you send in the 'suicide squad' but in all other circumstances it's impossible to know.
E.g. if cops try to stop an armed guy driving a car, and they eventually get him to stop, and the guy gets out the car ignoring commands and waving a gun … how would the cops know whether that guy is suicidal or homicidal?
^^^ And remember, the cops often have to make quick decisions in a split second. <--- it just wouldn't work.
Bottom line: citizens should live within the law and comply with officers of the law. This should be taught explicitly in schools, if necessary. Y'know, 'Citizen Studies' or something similar.