You can walk into the grocery store and buy eggs in a completely anonymous transaction, unless you want to use your debit card or for whatever reason sign up for their stupid loyalty programs. Point is, it's easy to do. Online commerce should have such an option too, especially since the presence of online stores could kill brick and mortar stores. If anonymity in online purchases were impossible that would be one thing (although then I'd just say online commerce wasn't yet ready for prime time), but the goal should be to have customers have all the same freedoms they had with B&M, one of which was anonymity. Now for physical goods, even if you solve the payment anonymity issue, there remains the barrier that you have to tell them how to get you the product, so that would have to be solved. I have an idea for that though. UPS and other shippers can have facilities to hold the goods, which they release to the first person with the proper code, no ID required.
Online shopping hasn’t done that much damage to B&M, and probably won’t. At the very least, most people like to touch the merchandise before buying. It’s a social experience for them.
It’s human nature, it’s why movie theatres are still selling out despite living in the age of Amazon Prime or Netflix.
… their stupid loyalty programs.
I have a card from Food Lion, it saves me on many products. I don’t worry about my purchases being tracked because I never registered the card.
With all the security cameras one must pose for on the way to the store, and while in it, and on the way out, the anonymity is only in effect until someone decides to start looking.