I'm not familiar with the validation associated with the passport system, but the problem with relying on E-Verify as it is now is that it is not designed to detect identity theft. All E-Verify will do (at least the last time I looked at it) is tell you that the social security number, name, gender, birth date, match. If an illegal immigrant has stolen someone's identity and presents an employer with information that matches, then E-Verify is going to say the employee is ok.
I presume that the passport system is designed more strictly to identify your identity, so really what you are talking about is more like a national identity card? A picture ID at the least, a biometric ID card may be better. Although I've heard that will not go over so well in some quarters.
Now the government could modify the system to start flagging SSNs that get multiple uses, but that becomes problematic. What happens when a person who actually is the real person that belongs to the SSN gets flagged (and possibly denied employment or has employment delayed)? If the government starts keeping track of multiple hits on the same SSN, then the government now has "constructive knowledge" that one or more individuals are at a minimum engaging in identity theft and likely not citizens (the main reason for engaging in identity theft to obtain employment). Now the government will be expected to do something about it.
Several years ago the SSA was going to start sending out "no match" letters to employers when the SSN's didn't match the employee information provided on the W-2's. The employer was then supposed to contact the employee and give them instructions on what to do (depending on whether the employee maintained that the SSN was correct) which could include going down to the local SSA office to sort things out. That program never got off the ground.