1A: "Congress shall make no law...abridging the freedom of speech, or of the press."
4A: "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
Wholesale banning of anonymous money transfers would also, in my opinion, be a violation of 1st and 4th amendments. But banning encrypted speech & communication altogether (or compelling an open-access backdoor) is clearly a violation of 1st & 4th amendment.
there's already enough cameras to capture every angle - including the ones at registers that clearly are there just to capture your face.
The only reason i can see for a cashless society is: someone is going to make shedloads of money on the microtransactions. Visa, MC, AmEx, JP Morgan, etc.
You can do that in the US though with cash. There might be some transactions that you can't do in physical cash but that is more of a practical/convince limitation and not a legal one.