Re: tax inversions
You are correct that dividends paid "up the chain" into the US entity would be subject to US tax; dividends paid out of the US to the parent might be subject to withholding tax, though frequently there would be a treaty reducing that substantially.
The foreign parent permits strategies that would not be avaiable with a US parent. For example, with a US parent, since a dividend is inefficient, one might consider having the foreign sub lend the proceeds to the US parent, but that would trigger income to the parent, because the loan would be an "investment in US property" which triggers what is called a subpart F inclusion. On the other hand, with a foreign parent, the foreign sub could lend the funds to the foreign parent, bypassing the US. And that would not be treated as an investment in US property, so no subpart F.