If we change to word "VAT" to tariffs on "all" goods (figuring that the vast majority of "goods" are made from imported content if not imports themselves), what would the pragmatic difference be?

At first glance, it seems similar with the added "whack the foreigners", but there are quite a few differences.
The US is a very big country, so a lot of stuff is mainly local origin.

For one thing, the rate would of course have to be much higher to raise the same amount of money overall.
It would cause much more distortion to the economy, for a variety of reasons (such as the above), probably the biggest argument against it. Very broad, very constant taxes have been shown to raise the most money with the least breakage.
It would of course violate a number of treaties, cheese off a lot of trading partners, and lead to retaliation of several kinds.
It is applied on import, not on end use, so things going back and forth across the border like car parts and cars can get hit multiple times.
It hits goods imported from US owned non-US enterprises, which may or may not be the intended result. They have a motive to close their non-US operations, which may currently be very profitable for the US.
In some ways, surprisingly, it's easier to dodge a tariff. Transfer pricing, services spoofing.
It is not as good as VAT at accomplishing a big macro goal of encouraging saving relative to consumption. (the lack of savings / excess of consumption across private and public sector is the cause of the US deficit and international borrowing).

Mr Colbert (the French finance minister of a previous century, not the TV host) once remarked that the art of taxation is getting the maximum number of feathers from the goose with the least amount of hissing. VAT and GST are, to date, the best in that regard.

To cut back on trade is to make people poorer in both places, by a lot. Imagine living your life consuming only those things produced wholly by your own household, or even your own city. Let me know when you've made your first integrated circuit : )

There are wonderful examples from my favourite historical economist, a Monsieur Bastiat, about some tariffs that were introduced on the fantastic new railroad between France and Spain. He pointed out that if using tariffs to reduce the benefits of trade were such a good idea, they'd be even better off simply blowing up the railroad. To those who thought that all exports were good and all imports bad, he pointed out that the logical conclusion was that everyone in the world would be better off if all the cargo-laden ships sank en route.

In short, it's not a good idea to gum up trade. A few deals are win-win, many are win-lose, but that one is a lose-lose.

Jim