I'll let our economy/stock market know that its obscene gains since the 70s shouldn't have happened.
Honestly, which is it?
Their breakneck avoidance to pay taxes/find-exploit loopholes has led to their success OR
They paid their unfriendly taxes all these years and still produced epic/unprecedented gains/success?!?
Your wording is weird and kind of ill-conceived, I think. I thought it was obvious I'm pointing to your first option as the choice of quite a few corporations. Yet you're writing this like there's some kind of Gotcha! dilemma that I've fallen into. If so, you didn't explain it very well.
Your statement here, as much sense of it as I can make, has a couple of problems.
1) A company can move a significant chunk of its operations--or even all of it--overseas, and still be publicly traded here in the US. Specifically, they frequently relocate manufacturing, and as you've noted, support. But it can be anything, and sometimes everything. As long as they meet certain federal requirements, they can still be listed on the NYSE and NASDAQ and form crucial parts of people's retirements and investment portfolios. So if someone says that rising US stock indices proves that corporations are bearing US taxes, there's a complication. Namely, that many publicly traded companies are not purely domestic entities whose profits depend entirely on US taxation.
2) We have a classic aggregation problem here. Just because some corps can and do stay, and remain very profitable in doing so, does not mean all corps can, or do. Crude example:
Company A moves operations abroad because US taxes are too costly.
Company B stays in the US and remains profitable.
Company C benefits from the reduced number of competitors.
Company D is a foreign multinational entity listed in the US.
The overall stock market can rise significantly, but the success of the aggregate market does not prove that every constituent firm found US taxes bearable. And similarly, if some corps leave because of taxes, the remaining corps' stock performances don't prove that taxes had no effect on departing corps. This is very close to the fallacy of composition, thought it's not quite it. I'd say the more precise issue is that aggregate outcomes don't automatically indicate what happened to each individual member of the group.
There's also the matter of risk tolerance here. Corporations are not static, uniform things. They have vastly different needs, mechanisms of survival, and pathways to profitability. That last part greatly depends on the risk tolerance of those running the show. Just because one group of guys says "We can stay here" doesn't mean the guys at the next corp are willing to say the same thing, even if theoretically they could.
Simply observing that the stock market has risen substantially over time is not sufficient to make your point. To argue that corporations can (or should) bear the brunt of US taxes and remain wildly successful, we'd need evidence like studies measuring the incidence of corporate tax, comparison of profits before and after tax changes, and evidence concerning wage effects, consumer prices, and capital mobility/offshoring.
For example, the US stock market has risen greatly since the 70's, as you point out, but corporate tax rates, among many other things, has changed. The market's rise by itself can't isolate the power of correlation within those various factors.
I don't know of any studies that would support your take, but I have reviewed a number of them back in my undergrad days that undermine it.