what types of student identifiers are you thinking?  

Student ID

Same with what has been said - that validation & audit are very important.  And the questionable reliability of data elements like PID/EID.  In practice, we also don't refer to students as their PID, it's their names that we use.  

Also important in cases of duplicate records for the same student - incorrect / no SSN or different name spelling - we see this a lot with students who once attended summer as a visitor and now matriculating at UCSD.  It is important to see the name and PID to make sure records are combined correctly.