This may be a problem for tracking orders.

The user may want to know in what state the order is, maybe change something after payment, return product, things like that. There is something reassuring about it too.

It is users who want to be remembered.

You do of course need to remember each order, keeping track of invoices etc. But I don't understand why that would require keeping track of a user more than any brick and mortar store that supports paying now and getting the product delivered to your door.

You need to authenticate the user to grant them access to the order info, no?

Not necessarily (as you wouldn't in a store); they'd just never to prove sufficient knowledge of the transaction (e.g. invoice number).

Note for example how you can track any package in the world when you know it's code. That seems to be working well without relying on user authentication, no?