Just for the record, I am not currently arguing with you, but I just thought I would point out something from real-world experience which starkly contradicts the "ideal" economic equilibrium you describe.
In my experience as a Norwegian, the parity argument isn't even close to true in the real world. There are lots of non-perishable goods here which are imported but are a lot more expensive than they are in the US. For reference, there is a 25% VAT on everything and there is occasionally an import tariff on the order ot 5%. Also some special taxes on vehicles, tobacco, alcohol and fuel, but I'll keep those separate.
Most goods here are a lot more expensive than abroad. Clothes and shoes are 2-3 times more expensive than in the US. Ditto for furniture and most non-perishable goods you would buy in a store. All food is 2-3 times more expensive, even imported, canned goods. This is in line with the labor required to stock and operate a store. Electronics are usually ~30-40% more expensive than abroad if you get them in the right place, which does more or less match the parity theory. My guess is that this is because buying these goods on the Internet is a viable option (in contrast to groceries, clothes, shoes, food, medicine, furniture etc). Hence these retailers are forced to conform, or go out of business. I am not sure how they are able to do this, whereas a clothing store or a supermarket is not. But this is what I observe. The cheapest electronics retailers are very low on staff and high on automation.
Long story short, locally labor-intensive products are obviously a lot more expensive in expensive countries. But higher salaries also have a very large effect also on the cost of imported goods, because there is a lot of labor involved during the shipping, import and sales process. If you are able to automate away some of this, you have a massive business opportunity. But it's a very obvious opening, so it is not a trivial task.