"Do we really need the user to set up an account with us when they might be buying a single item and just want that, right away?"
In the Bitmenu system, user accounts are for customer service purposes. We track each purchase and help buyers resolve issues. Since we make such lightweight use of accounts, we set them up automatically and in the background.
"If a user gets a tweet or email with an offer to purchase something, wouldn't they prefer to use a payment method they already trust and use regularly?"
Bitmenu currently offers purchase using Amazon or PayPal credentials. Our system does not hold funds but acts as a broker and agent for our Sellers. Buyers are sent to Amazon Payments or PayPal where they authorize the purchase amount and then are returned to us for fulfillment. The user presents their credentials to our payment partner, who then validates the purchase to us in the background.
This video from Google illustrates some of the issues we address with our system.