Earlier quoted context omitted.
My hunch is that the store wasn't meant to be particularly popular with lots of customers, it was meant to demonstrate technologies they wanted to sell to businesses. https://aws.amazon.com/just-walk-out/ https://aws.amazon.com/one/
They've employed a "Amazon is the first and best customer" for most of the services they've launched. Amazon.com / AWS is an example.
Like the eBay Pez story it makes sense and adds credibility for the narrative to be that Amazon was the first customer for AWS. But it feels like a very unamazon thing to do, given that so much of its customer base isn't running the kind of enterprise jobs that an Amazon scale company needs.
(Either way I imagine almost all of Amazon does run on AWS these days and I'm sure the transition took a long time)