Often the actual laundering process is done by a third party who takes a cut. A middleman who provides money laundering as a service to criminals. Under your scheme that person wouldn't be committing a crime and could not be prosecuted.

But that's beside the point. The crime isn't "moving money around in unconventional ways," it's lying to the IRS and other government agencies. It's signing your name on all those tax documents that say "under penalty of perjury" after filling them in with false information.