And now your "simple" solution is complicated because the carriers don't know what's inside the box they are shipping (unless it falls into a prohibited or dangerous class of goods that require special handling).
And you still haven't solved the classification problems. Biologists debate the taxonomy of known species all the time (see bison bison bison vs. bison bison athabascae) and you think there's some simple way to classify manufactured products? Even Amazon hasn't solved that problem.
Even if you could come up with some magic taxonomy for manufactured products it still wouldn't work for taxation because the tax laws in even a single jurisdiction are riddled with exceptions for certain buyers, or for different types of use. For example, buying a sandwich at Subway "to go" is not taxed in CA because it's considered groceries and not a served meal. But if it's a hot sandwich, you eat-in, or you opt to have the sandwich toasted, and it's taxable as a meal. Buy the same sandwich at the grocery store deli, and it's not taxed because it's groceries. Unless they package it as ready-to-eat and have picnic tables and suddenly it might be taxable and depends on how they wrap/package it. In some jurisdictions the soda that came with your meal has a tax, but not if you got ice tea or lemonade out of the exact same fountain.
That's just one state, with just a simple fast-food meal. And isn't even including the counties, cities, special taxation districts, etc that all complicate it further.
The only way to make this work is to rip it all out and replace sales tax with a Federal standard (see Europe and VAT), and that's not gonna happen.