While it takes much imagination to find that 8 U.S.C. § 1324a(h) gives the president unlimited authority to allow aliens to work in the country, the plain text of § 1182(a)(5) explicitly gives the executive the power to exclude aliens who “adversely affect the wages and working conditions of workers in the United States similarly employed.”
Imagine the next Disney situation when an employer tells hundreds of Americans they are being replaced by foreign workers and have to train those replacements to collect unemployment. Those workers then complain to the Department of Labor. Instead of encountering an unsympathetic President Obama, Bush, or Clinton, a patriot like President Donald Trump could step in and deport the foreign replacements. Even the New York Times editorial page would have a hard time criticizing President Trump for such an action.
The next company that tries to pull a Disney could find itself left high-and-dry with its foreign workers getting the boot from the country.