The core problem is that there are so many things that can help prevent the problems from arising to begin with that need to be done before policing is even considered. Better healthcare, housing, education, etc. Police are, at best, a last resort solution to desperate cases, and they tend to be hammers looking for nails as a result. It might be possible to do it well, yes, but it's very hard, and you should really be looking for a less antagonistic solution first.

To take your idea of "speeding at 100+" as an example: This could be solved by replacing cars with public transport, such that people don't really have so many opportunities to go 100+ to begin with, or by using traffic calming techniques to make it feel too unsafe for anyone to want to try, or using alternative road layouts to make it significantly harder to pull off at all (e.g. roundabouts). There are many options, almost all of which are better – and less punitive – than the police.

Also, tangential, but...

crisis councilors aren’t going to be driving trying to perform a PIT maneuver.

Of course not; PIT maneuvers would kill people.