The government has had practically zero control over cash transactions, historically speaking. The only real power governments have over their money supplies are the power to create and destroy money with impunity, that is all.
Government has had extremely tight control over cash transactions.
1. Try to give someone $100,000,000 in cash. It literally weighs over a ton. The government stopped printing bills > $100 in 1946 explicitly to control cash transactions. With inflation, the largest bills we have to work with are worth about $30 in 1946 dollars.
2. Look up AML and BSA legislation, "Know Your Customer" regulations, Form 8300, Structuring Deposits. Did you know that a bank has to report you to the government if you deposit more than $10,000 in cash? And that if you deposit $6,000 on a Wednesday and $4,000 on a Thursday with perfectly legal money in an attempt to avoid the reporting that you have broken the law? (https://www.irs.gov/irm/part4/irm_04-026-013#:~:text=Structu....)
3. Try to open up a bank account and tell them you'll be depositing lots of cash. They'll refuse to open an account for you.
And admittedly this is today's U.S. government. But governments haven't just taken a "oh well" approach to cash ever in all of history.
Is this a common problem? I don't normally transact $100M on a normal basis, and the few times I've transacted anything more than even $5k or so usually involved some form with the government involving a title transfer or something along those lines. So then the argument of needing to do it privately is a bit of a moot point anyways.