Or better training and actual accountability. It's not like cops use tasers judiciously and intelligently.

Possibly.

But, another name for “non-lethal weapon” is “cheap and effective compliance tool”.

With those, we risk making many forms of protest and civil disobedience difficult or impossible.

How about using electro-magnetic waves to alter the brain function temporarily and provoke it to lose consciousness? Sounds like a hard technical challenge, but we can already deliver effective tranquilisants remotely and use electrical discharge to disable the central nervous system. Just find a more efficient way of doing that.

Ideally you would want some kind of sci-fi weapon that shoots out some sort of impenetrable web/blanket that wraps around the criminal, holding them until you can safely handle them at a later point.

It's mind boggling that a centuries old weapon is a supposition for any problem, let alone such a terribly serious one. It's likely that dog catchers are more advanced in their approach.