Form I-9 has een in olace since the late 0’s or early 80’s. The fine for hiring anyone without clearing that form FIRST is $5000 a day per employee.
I could not even put MY MOTHER on payroll without her filling out an I-9 correctly & completely.
You are right that the I-9 system has been in place for almost 40 years. It is too easy to use easily available false documents to beat that system. Even a school ID with a picture can count as partial verification.
What would be effective, I think, is using the I-9 to track the use of false Social Security numbers. Immigrants use numbers that other people give them, resulting in Social Security taxes being paid from multiple, geographically separate locations under the same number. It would be child’s play to follow up on those employees who use repeated numbers. But currently, the Social Security administration just keeps those erroneous payments and, apparently, says nothing to immigration enforcement agencies. It helps their budget, I guess.