I appreciate the clarification. The current process with Shopify POS is that you can store customer information as mentioned above, but you still need to search for the customer when processing the sale. This happens before the customer pays. When you go to the cart, you can select “Add customer”, and then you’ll have the option to search for existing customers rather than adding a new one each time.
I totally understand the feature you’re requesting, as I have used Square checkout before and get my receipts emailed to me. I’m happy to share this feedback with our developers for consideration in future updates.