I wouldn't want to give my SSN out to a store. At least with a credit card, I can cancel it fairly easily. The more sensitive the information you're required to give, the more cautious people will be about buying. People might trust a well-established company like Amazon but the smaller etailers would be out of luck.
Maybe if your PGP key was also tied to your account with the shop, that would be a bit of a disincentive. It's harder to make a new account every time if you have to tie it to a credit card with a billing address. If someone tried to make multiple accounts with the same billing info, that would be a red flag.
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