This is specifically an issue of international repatriation and has little to do with anything else really - and your OP doesn't really aim at that.
Amazon is a poor example because they're not in the business of fancy IP arbitrage: this is what Apple, Google and FB do. Less so Amazon.
But the problem is that US taxation with respect to repatriation is messed up.
1) US corporate tax is very high - the highest in the developed world. 2) US expects companies to pay 'full tax' when repatriated money, even already taxed money. Every other country just expects a 2-5% repatriation tax.
The US tax system is not designed for globalism.
What the US and the world need to do is find a new harmony which will entail:
1) Lower US corporate taxes 2) Close all the special loopholes 3) Get rid of double-taxation on remuneration 3) Especially for digital and IP - taxes need to be paid in the local state where business is done. FB is selling ads and consumers are consuming them in France, then a good chunk of taxes need to go there. Same for Google. The US is going to have to eat this or face punitive war forever from EU and other nations.
If Apple has no reason to recognize profits in the US, I assume Matsushita has less reason to, so it doesn't really matter if foreign companies don't pay out to the US. If anything, it makes it more useful for the US government to prefer to give business to US companies.
I'd love to see how one would "close all the special loopholes" and force the companies to "pay taxes in the local state where business is done". This is exactly the problem. You reacted to the "ideology" of having a government share of the company, but your solution would require a much more invasive bureaucracy to accomplish the goal.