KYC, anti-laundering preventions etc. They wouldn't take it down just because they think that it broke law, they know it.

I'm not an expert but if the accounts that were created did check for the user's identity papers beforehand, would the mixing of the cryptocurrency be illegal in itself? How would the platform know the origin of the money?

Not knowing the origin of the money is the crime here. You're explicitly not allowed by law to look the other way.