To whom would the US issue green cards for pilot jobs? In your opening, you noted that Europe does not have enough pilots with those qualifications already, hence the airline cadet programs. China, Korea, India, UAE, and other Asia and Middle-East countries are already recruiting away from the US and Europe.
To start, those US pilots now attracted to Asian/ME jobs will find US jobs. Then more military pilots will leave the military early to get more-in-demand, higher-paying airline jobs. More "universities" will crop up and devise programs to satisfy the education option.
In the longer term, corporate and Netjets-type jobs will become more entry-level "jet jobs," and the airlines will recruit from them. Still, there is a good probability of a shortage of qualified pilots 5 or 10 years from now, and US airlines may try cadet programs as well and/or subsidize General Aviation with incentives to earn ratings.