Crime comics are morbidly close to horror in many ways. Though it was necessary to argue in court art vs gratuitous display with a decapitated head; not necessarily out of repugnance for this so much as that it was more immediately shocking, and easier to build a case against, than the more nebulous (but perceived) notion of encouraging delinquency in the readership.
I do think that breaking every plot down to Good vs Evil is biblically overdetermined. Good vs Bad perhaps, since true evil extends beyond the bag snatcher IMO.
Crooks in comics, as in many works of fiction, are useful for telling a story. They act as a quick counterpoint to the protagonist. The early costumed heroes had a steady supply of generic hoodlums with hats and guns to contend with.
The ongoing debate as to whether the depiction of burglars and kidnappers has a deleterious effect on impressionable minds has to be tempered by explicit statements that Crime Does Not Pay and with Batman's famous motivation for choosing his identity:"Criminals are a cowardly and superstitious lot".
There hasn't been as much use of the uniform police because there is an attraction to a more vigiliante approach to law enforcement (if you can even call busting someone's jaw for a holdup 'law enforcement').
Private eyes and gumshoes have seen their turf taken over but there's been a resurgence of late.
And bank robbery and slayings remain popular staples.