The website actually asks for SSN to identify teachers?
The SSN wasn't supposed to be used for identification at all, at first. [1] But the government decided that didn't apply to them, and then they decided that it didn't apply to anyone else.
1: https://www.nytimes.com/1998/07/26/weekinreview/the-nation-n...
BTW, California has a similar website that allows employers to put in SSN and DOB to lookup a teacher's license: https://www.ctc.ca.gov/commission/lookup
It seems that Missouri had a similar setup that required a teacher's last name and the last 4 SSN digits.