As somebody that has gone through the whole process (MS, PhD, OPT, H1B, Green Card), granting green cards to diplomas of is a big mistake. While the current system adds some level of stress to the worker, I have yet to find (surely there are) a valid foreigner with some STEM degree that could not stay in the US if he wanted to. This is true for most "bad" students that I know. On the other hand, some students that trick the system (most of them, in my experience [1], chinese and indian) have had trouble to stay.
The current system gives you up to 29 months in OPT after a STEM degree (if I recall correctly, 12 + 17). During that time you can work towards H1B and Green Card; while H1B is tight with a employer, you can change employers with it. Now, if the Green Card is given to any STEM diploma, you will have a mass of unprepared, unethical students applying for and obtaining diplomas they don't deserve (because obtaining a diploma is not that difficult in the US). And I do believe this will create tensions later on with nationals.
[1] This is obviously biased. My experience in the university (and outside of it) is that there are networks that facilitate entry on universities, "success" in universities [2,3], and in interviews processes in companies. I have seen exams for the previous 10 years solved with detailed explanation; homeworks and all solutions for specific books solved, etc... with this only available to specific group. I have not seen this happening with people of other countries.
[2] http://www.cnn.com/2015/07/12/asia/china-education-agencies/
[3] http://www.reuters.com/investigates/special-report/college-c...