An issue with this is that the print CSS of most websites is an afterthought.

While it’s possible to alter the design with @media print as well as the page breaks, few websites do this. You are often left with broken layouts, empty pages, or nonsense page breaks.

For some insane reason, one of the stores we use that you can order online and pickup at the store, when you try to print the page with the barcode, the barcode does not print. We end up having to take a screenshot and print that. It's just utterly baffling, especially for this specific use case.