This feels plausible but I think it is really nonsense.
Processing fees are not unique to cash. Banks charge cash processing fees to businesses too, and have for ever. Most shops will deposit all the cash received at the end of the day - perhaps every few days - with a bank.
That's true- everyone with a checking account pays a "fee", even if that's in the form of "allowing the bank to loan your money out to make more money"... except for maybe USAA. Their checking accounts are free, no account minimums, and they even pay a little bit in interest. Not just anyone can get a USAA checking account though so I guess that doesn't really count.
So long as you don't use a brick and mortar bank, most banks have interest providing checking accounts, although rates vary wildly.
Savings accounts in particular are egregiously terrible at brick and mortar banks. I made more in interest payments in my first month at Ally than I did in the ten years I had my child hood savings account at Bank of America.
Those cash processing fees would only apply if the cash was repeatedly deposited and withdrawn, and probably only by businesses. The hygienist can probably deposit cash for free, I don't think I've ever paid a fee into a consumer bank account.
Taxes will do the same, though. Employers have to payroll taxes, employees have to pay income taxes. The $50 will eventually all bleed back to the government.