Billing address as an authorization token...

So I've noticed now that I have more than one abode, that online merchants frequently use your billing address on your credit card as an authorization token, without herculean effort that is the only address they will ship to.

This presents a problem if you are shuttling between states. Sensible merchants (IE Amazon) can cope with someone shipping to an address you don't reside at (how else does one send gifts) or event sending multiple items in the same order to different locations.

But my biggest issue ultimately is that as indication of authorization to perform an action billing address is a pretty poor token. Digital signatures have basically failed in the consumer space if that's the best we can do frankly.

On the face of it identity theft involving moving mailing addresses doesn't seem that hard, or maybe I'm missing something.

You can of course add additional shipping addresses to credit cards and many retailers will accept those but how many addresses do you have to have (6 or 8 ) before you can't remember which address is associated with which card?