How did things work under Clinton, Bush, and Obama?
When the 2016 rule was proposed, the stated purpose was to enhance H1B portability by allowing workers to find another job to try to stay in the country: https://www.federalregister.gov/documents/2016/11/18/2016-27...
“60-day nonimmigrant grace periods.
To further enhance job portability, the final rule establishes a grace period of up to 60 consecutive days during each authorized validity period for individuals in the E-1, E-2, E-3, H-1B, H-1B1, L-1, O-1 or TN classifications. This grace period allows high-skilled workers in these classifications, including those whose employment ceases prior to the end of the petition validity period, to more readily pursue new employment should they be eligible for other employer-sponsored nonimmigrant classifications or employment in the same classification with a new employer. The grace period also allows U.S. employers to more easily facilitate changes in employment for existing or newly recruited nonimmigrant workers.”
The rule didn’t say that there was a meaningful problem with employees having to depart the country instantly upon losing their jobs. That’s telling, because when a notice like this is published, agencies must articulate facts to support the rule change. If this was actually a problem the agency would have mentioned it.