I don't see why beanbag shotguns or weapons along those lines can't be used, I'll tell you right now a swift high velocity bean bag to the bollocks will take out the biggest 300 pound weight lifting son of a *****.
Firearms are by no means a necessity and introducing them will just make criminals all the more dangerous, as they'll be infinitely more willing to arm themselves too, it may make the police more effective at responding to situations like those posted by the OP, but then you've got the problem of there being more armed criminals, so is the trade off really worth it when you've got non-lethal weapons that, as said above, will take down the biggest, 300 pound weight lifting son of a ***** and reduce them to a crying child?
Hell, beat officers in our town now are carrying tasers and I STILL think that's a better option than firearms.
If they absolutely MUST carry them, leave them to very specialist divisions with exceptional training in their usage.