"Mixing" is bitcoin speech for "money laundering" and it doesn't end well for whoever is doing the laundry, no matter how much technobabble you put on top of it.
Mixing is not laundering. Money laundering is about converting money to something that can be passed as income from legal transactions. Mixing is only about disguising where the money came from (which is something that you essentially don't have to do for physical cash)
What on earth is money laundering if not disguising the origin of lots and lots of physical cash? As always, a lot of this has its origins in drug trade.
Money laundering is disguising the origin in general, which is of course the point of mixing. It's not some kind of theoretical bitcoin boner exercise, it's intended so you can maybe at a later date withdraw some bitcoins without the party providing the cash (and the feds) immediately making the connection to the crime.
Money laundering is not about simply disguisng the origin, but about disguising the origin such that it looks like some legitimate (typically taxable) endeavor.
Bitcoin mixing disguises the origin only as far as the blockchain is concerned, you still end up with X BTC that you have no explanation for how you earned them.