Don't be naive. LocalMonero / LocalBitcoin is prime way to launder cash for organized crime. A thousand dollar here, a thousand dollar there, then you have converted your money to crypto.
A thousand dollars here and there doesn't get you anywhere. And really, you'd have lots of risk -- if money laundering was the primary application, the police would surely join the fun, and if you're not meeting a cop, there's a good chance you're meeting a robber that knows you'll be arriving with lots of cash.
But the amounts really don't make sense. Organized crime is certainly not running around making $1000 deals all day with different people to somehow launder money by converting it into bitcoin and back ("I found this bitcoin on a sidewalk on the internet and I've exchanged it for cash, so now this cash is legal?").
You go on localbitcoins and trade your cash for bitcoin (fully legal) and then buy drugs from me via darkweb (fully anonymous).
I sell you the drugs on darkweb (fully anonymous) and then offload my bitcoin on localbitcoin for cash (fully legal). This removes a lot of risk for both parties
This is the original business model, but the authorities caught on pretty quickly and implemented all of those pesky KYC/AML requirements.
Not very anonymous unless you're really careful about it and never fail once. The localbitcoins person is linked to everyone they interacted with, and the transactions are public and timestamped. Unless you use a new address every time, your identity can be deduced fairly easily from your other activities.
The probable result is that the police nab the localbitcoins person, then pressure them to explain who they were doing business with, and go from there.
If anything it's worse than buying drugs in a dark alley because there's a permanent record of your activity.
A thousand dollars here and there is not how these guys launder money. That's not noteworthy at all to authorities. It would put like the whole population under the radar. Authorities start to check things out at the $10k range.
But the amounts really don't make sense. Organized crime is certainly not running around making $1000 deals all day with different people to somehow launder money by converting it into bitcoin and back ("I found this bitcoin on a sidewalk on the internet and I've exchanged it for cash, so now this cash is legal?").