Depends on the detectives. Some might be willing to put forward the effort for something like that. Some will just look at it as more worthless paperwork and not bother.

Also depends on the crime. Something that hits the Detective's buttons, he'll do it. Meh, he won't.

Again comes down to not having carte blanche to run amok. You start killing large swaths of people to the point it becomes a political issue and the case won't be given to the lazy detective, those detectives get the lamo Burglary and other larceny cases where you'll be fine with erased if you oops and leave some evidence behind. But again if you go on a stealing spree where it becomes a political issue bring out the hot shot detective again.

That's true of anything, really. Erased or no erased. But your point is made.