Regardless of the distinction between sales tax and VAT, if any given US state wanted to have the state sales tax be included in the price that is shown to the end-user (at least in physical stores that exist in that state), I don't think there's any federal law preventing them from doing so. In other words, rather than having the store list a pack of gum for $1.00 and then charging me $1.06 at the register, the state could just require that the store list the pack of gum at $1.06. If that means the price of a can of Arizona Tea has to vary by, like, two cents when you cross state lines, that's a worthwhile tradeoff.
Sales Tax rates vary by the address and don’t apply to some goods/services. Additionally, some states have holidays (like “back to school no sales tax days”).
That is to say that the retailer needs the recipient’s address before shopping, rather than after. Also, if sales tax is handled by an external API call, those costs would increase drastically if the same call must be made for each product listing price, as opposed to just a few at the end of checkout flow.
The bajillion-jurisdictions problem can be solved on an aggregate basis.
Charge everyone $100 inclusive-of-taxes. Keep $93.50 of that from a customer in Phoenix, $92.75 from a customer in Los Angeles, and all $100 from a customer in Oregon. If you have approximate knowledge of how your demand breaks down, you could come up with an all-inclusive price that produces the average bottom-line revenue you want.
You seem to be hand-waving away the accounting part and the fact that the subtotals for the same goods will be different for users in different cities.