Lets say for the sake of argument that you are right, and the no. 1 use case of cash is to evade taxes. Then the people getting payed for their tax-free labor will need to use this cash somehow. The easiest (and cheapest) is simply to circulate the money while buying regular goods and services. So buying of regular goods and services would rise to be at least as popular use case of cash as tax evasion is.
Also note that there are plenty of people willing to pay tax for their transaction, but the transaction is made illegal by their government and hence they cannot. Then the reason to use cash is not tax evasion, but illegal transaction, (note that this includes paying and receiving salaries for people not allowed to work because of immigration status). Tax evasion then becomes a happy byproduct of the no. 1 reason for using cash, illegal transaction.
But I honestly doubt that either illegal transactions, nor tax evasion comes even close to why most people use cash. Convenience. Though I could be persuaded if I saw some data pointing to the opposite.
The fact that lots of people in India have had serious issues because they were unbanked does seem to indicate that there's a sizable population of people using cash for everything*. I'm curious if there's any research into whether that's for tax-evasion reasons or for some other reason.
My personal belief is that the number one use is for money laundering, and that people who are using it that way would be willing to pay taxes on the money they are laundering from some other illegal activity. For instance, there are all-cash drug dealers who pay taxes on their drug money. I'm sure Al Capone wishes in retrospect that he'd paid taxes...
Have you ever experienced a natural disaster? One thing you realize quite quickly is that your debit card is useless. That doesn’t mean transactions stop, people are still buying and selling, those with cash at least. If there’s runs on banks, infrastructure outages, etc, those relying entirely on debit and other payment cards won’t be buying food!
That's like $1.2 trillion in boring, normal, law-abiding cash transactions each year.
Also, for the record, I have been in and responded to a number of natural disasters in the "first world". With the exception of a few hours here and there, using cards was never a problem. If the infrastructure is so wrecked that cards don't work, food/water is coming from people in high-vis vests.
Try a hurricane, or something serious enough to be registered as a natural disaster.
I’m sure there are ways to use cryptocurrency to do the same.