Can't speak to the US situation, but here in Canada there are anti-money laundering "know your client" rules for securities brokers - and securities are far more regulated in the US than Canada (Canada has no equivalent of the SEC). You can't just buy millions of dollars of publicly-traded securities through an anonymous shell corporation.

No such rules exist for housing that is purchased outright and not financed.

These people don't want an investment, per se. They need to store the money, but also to hide it. If the beneficial ownership of the assets purchased with the money is obscured, they can't be clawed back if they are arrested in China and charged with stealing that money in the first place.