This is just an Amazon site issue, lots of things are broken right now. This problem specifically appears to be caused by the site not being able to determine your location to ship to.
Why should that matter for anything but the shipping price, which shouldn't even be needed on the product page?
Exactly. The usual pattern is to calculate shipping "during" the checkout phase, not before. i/f a customer demands to know it earlier, the site can always ask for shipping details separately and show the final price on the same product details page.