From a security point of view, you have no actual control over whether plenty of merchants and customers trade using counterfeit money, and so you have to maintain a large set of infrastructure around finding and punishing people who use or accept counterfeits.
You can have all the tech for proving that a dollar is legit, but it nobody cares if the dollar is legit, then it doesn't matter
You can have all the tech for proving that a dollar is legit, but it nobody cares if the dollar is legit, then it doesn't matter