Using a ton of different cards indeed would sound like a database leak to me, so with the retailer being liable for the user's and/or bank's failure to design a system under which the user can keep their credentials secure, this behavior being not allowed is understandable. This is all relatively foreign to me as a European who just pays with iDeal (Dutch system) that doesn't know fraud chargebacks or anything, and where it's on the banks (rather than retailers) to refund fraud from e.g. phishing so it's in their own interest to design a secure system, so correct me if I misunderstood something about how credit cards work.
The "single click" is in fact super annoying in my use case. I have an account with Amazon, with two different cards, one for professional purchases and one for personal ones[0].
When I buy a physical thing I can choose the card when paying. But for Kindles that's not possible, so I have to change the default card before buy. Very annoyging.
Also, for some reason, as described by the OP, one can't add a Kindle book to any cart to buy more than one at a time... or even save it for later! Which is completely absurd and user hostile.
[0] It's also possible to have two different accounts, but that comes with different problems; I have a pro account with Amazon but never use it.