Building a new card network akin to Visa would be a monumental task. You'd be better off lobbying for legislation.
If you buy in a brick and mortar store the retailer would not have your address, only your card number. And a privacy-focusd CC company would allow you to generate new numbers for each transaction so the retailers can't use that to merge datasets.
Google is now closing the circle to get to know exactly what was bought - blowing all privacy advantages away.
1: https://support.google.com/pay/merchants/answer/6345242?hl=e...
An untapped opportunity perhaps
The only problem is that the total you can spend: ~$50 on the ones I've found, so not terribly useful. But it's at least proof of concept that they could do it if they wanted to.
Japan is mostly (for the moment, anyway) a cash based society, so these kinds of things work. Payment cards are becoming more and more popular, where you load money on to them and then you can use them in stores. Most of them don't require that you register with them, but of course they all recommend it (and you can't take money off of a card without it being registered, presumably to reduce theft of the cards).
I quite like the system, since I like privacy. Also much better than a debit card since I don't have to give access to my primary bank account to have a convenient payment system.
But even if some company offered that all the retailers could still share their data with some aggregator which would effective work around your privacy oriented card not sharing data.
I'd love not to be tracked and would switch cards immediately if they offered the same services I get now and offered zero tracking. I suspect I'm in the minority but maybe with the right PR blitz you could get regular people to switch.
"Does your credit card spy on you? Do they sell all your purchase data to advertisers so they can target you with ads? Yes? Welcome to 'PrivacyCard'"
or something
Next YC batch?