"Make Amazon's Customers Your Customers"

Except this is on your web-site and you would be making your customer Amazon's customer.

There is a deep conflict in this solution, and no doubt some people will jump for it not deliberating on what it could mean for them.

For me this represents a shift away from payment processing (Stripe, or even PayPal), and towards ownership of the set of master records that power an online commerce business. There is a fine but clear line between helping to process a payment and taking over the ownership of the customer. This is your customer, not Amazon's, and the master record should be in your hand and leveraged by you, not Amazon. I would be very hesitant to walk this path.