It's creating a paper trail for the prosecution when the feds decide they want to take someone down.
It's not money laundering per se that the feds have an interest in prosecuting. They have an interest in prosecuting sanctions evasion, tax evasion, black mail, drug smuggling, etc. It's the source of dirty money that they want to stop, not the dirty money itself.
What happens is they think someone is smuggling drugs. They see they have money, the money looks suspicious, they get a warrant from the bank, they give them all their AML/KYC forms, and the feds go and track down the real source, and find out that the forms were full of lies and now they can get the drug dealer on bank fraud charges -- which means they don't need to connect them to drugs or murders or anything else, even if that's the real reason they're interested in them.
AML/KYC stuff only prevents crime in that it forces criminals to commit other, easier to prosecute crimes to cover up their original crimes.