Right now crime feels very binary. Either you have a normal planet, with decent conditions (home-job-amenities triad), so that government building provided enforcers + even lvl 3 governor are more then enough to keep natural pop crime. So in this case crime is literally non-issue for you, no events, no effects, nothing.
Or you have recently conquered/blockaded planet, with crime levels above 30. In which case you fix the needs triad first - and then just wait a bit. Because, again, government building enforcers would take care of base levels + a bit above, so crime would go down. Since reason for the crime is bad situation on a planet - thing you could easily fix.
Third example would be crime syndicate, but all that does is artificially inflates your crime levels. In which case you just need to temporarily increase your crime suppression - precinct or 2 usually does the trick, maybe throw good governor and martial law in the mix.
I feel the only way to make crime somewhat an issue for everyone (and let's be honest, crime is a factor no matter how good or well-maintained you society is) is to change enforcers from -20 crime per work slot to -10 and -10%. This way you can have a choice - having few precincts to cull all the passive crime from pops. Or have, say, 1 precinct+capitol building, which would give you 40 flat and 40% crime reduction. So effect of crime would be very small, even negligible, but the crime would still be there. That being said tho, if crime effect would be negligible with just 1 precinct, so why even bothering with splitting crime fighting values in the first place..