Those corporations haven't "left the US."
What most of them are doing is exploiting a tax loophole. They purchase a foreign company, and use the merger process to reincorporate abroad, and cut their tax rate by a few points.
The
effective corporate tax rate -- as in, what they actually pay -- is actually fairly low. On average it's around 12%. When you include all taxes (local, state, foreign, federal) it's around 17%. (
GAO: U.S. corporations pay average effective tax rate of 12.6% - Jul. 1, 2013)
BK appears to be an exception. They are in an industry with a higher tax rate (effective rates around 27.5%), but they actually won't save much by moving to Canada -- Tim Horton's rates are reported between 27 and 29%. They might save a little on capital gains. (
Burger King Deal Draws Tax Criticism - WSJ note may soon be paywall)
Shareholders seem to like inversions... for a few weeks. Stock performance doesn't actually improve after doing an inversion. In addition, some shareholders can get screwed by the process. E.g. if you bought BK at $14, and the company does the conversion at $30, you get issued new stock -- and likely have to pay capital gains at the conversion price. (
Burger King merger: Do 'tax inversions' really make sense? (+video) - CSMonitor.com)
The US isn't the only country where this happens. Amazon, for example, has avoided taxes in EU nations for years by incorporating in Luxembourg. The Brits were supposedly pretty ticked off about it, too.
Amazon: £7bn sales, no UK corporation tax | Technology | The Guardian
No one is moving because of any politician's rhetoric; that's just silly. None of those companies plan to stop doing business in the US. BK is not going to close stores in the US. All of those companies still have to deal with the US tax code, US regulations, US employees, US customers and so forth.
The reality is that most inversions, and corporate HQ location changes, are for tax reasons.