The trouble is the stuff that is bad-by-design: the fact that it's even more expansively invasive than the existing 'loyalty card' schemes
I keep hearing this and I don't understand it. How is it any different than the majority of people who use the same credit card at different stores?
It is very illegal for a merchant to store your credit card number for more than the 5 seconds it takes to authorize the transaction, unless they implement fairly strong protection to make sure nobody can steal those numbers later. But even if they do this, it is still very illegal for them to try to share those card numbers and what they purchased, which would be necessary for different merchants to "track" your purchases.
CurrentC probably does not have this protection. Merchants would be free to store and share the fact that your CurrentC account number bought X here, Y there, and Z there. Merchants would love that ability, which is why they've designed CurrentC to allow it; as a customer, you have very little to gain from that kind of data mining, and almost definitely plenty to lose.