For your system to work, everyone would have to report all their purchases.
Wrong. The business is responsible for collecting the tax. The purchaser bears no responsibility for the actions of the business. States do a competent job of collecting sales tax and watching over it. The national retail sales tax (NRST) would be much the same.
See my previous posts for the difficulty of enforcement. I'm not sure how competent VA is at my flea market. I have bought many items that would be hard to track. One example is CD's and tapes, some of which are probably bootleg. I pick out a small pile, negotiate a price, the vendors puts them in a bag and puts my cash in his till. I don't know how many units he sells or buys wholesale. I don't know if he steals from the till or counts it accurately. How is the state going to know this?
My concern is not that they couldn't figure out a way to enforce this but that in the process of enforcement they would eliminate all "illegitimate" vendors and possibly eliminate my ability to buy anonymously.