It's how the EU today works BTW. In german shops you can buy locally produced pasta or imported Italian pasta (no import tax), both with 7% vat on it. Now you can claim "but this is EU...".
Why can't this free trade be done with individual countries for specific products then?
You and the parent poster are talking past each other. They asked:
> Why would there a VAT on, say, domestically produced pasta on the grocery shelf, while the Italian import pasta right next to it has none?
You answer (correctly) that that isn't the case, both boxes of pasta have the same VAT applied to it.
In light of this, I think people are really struggling to understand what you're arguing for or against here. The whole subthread started by someone pointing out that the 10%-for-everyone version of trump's tarrifs is very different from European VAT, since European VAT applies to all products sold to consumers, regardless of whether they are imported or not. That is, indeed, a vital difference. You seem to argue that it's not the case, while giving examples of how it is the case, leaving everyone confused.
Why can't this free trade be done with individual countries for specific products then?