Why the ruse? (obvious spoilers)

this may seem like a mildly silly question, perhaps I've missed something, but in any case I'd like to hear others' interpretations:

The 2 killers seem like the psychotic, violent, sexually-aroused-by-their-actions type of people. That is at least the impression I was given by their style of crimes, rather than the type to play mind-games or whatever.

So basically the entire process they go through - the false identities and the recorded & isolated interrogations of suspects - something that would require planning, scheming, even finesse, just doesn't sit well with their MO as I see it.

so my question(s) are simple: what is their motive here? to get the cop to confess about being fooled into killing his partner? to kill some more people? to destory evidence? more voyerism 'material'? those could have been done without the elaborate hoax that followed..(well maybe not the voyerism). so I'm inclined to think it is something else Ive missed (or maybe just that there'd be no real plot or twist without this ordeal?)

anyway, dead tired here & feeling a bit crappy but thought I'd ask anyway, all opinions would be appreciated, thanks :)

oh, and one more little thingy (aside from numerous other plot-holes) - why did the little girl, upon discovering their true identity, would mention it to the killer, and *hug* the other one?