What is the benefit for getting the new (updated) card. I've never changed my SSN card since I was a student, when it must've had these restrictions as well. Any benefit in changing after citizenship? No one ever asks to see it. Just wondering if I am missing something.
The benefit is not so much in getting an updated card (although if your current card has a notation "employment authorization required", then getting a new card is certainly a plus), but in getting your info updated in the Social Security computer system, so that your U.S. citizen status is reflected there. Most local Social Security offices will send you a new card when you update your status to a U.S. citizen, even if you do not request a new card.
Also, after getting a U.S. passport, you should file a new I-9 form with your employer, updating your status there to that of a U.S. citizen as well.
Employers periodically get audited by ICE for I-9 compliance and if they find a discrepancy between I-9 data and the ICE/USCIS/Social Security data regarding your status, both you and your employer will get into some trouble.
Moreover, more and more states require various categories of employers (and sometimes all employers) in that state to use the E-Verify system to check if a person is authorized to work in the U.S. The use of E-Verify will likely become more and more widespread in the next few years.
When E-Verify discovers ANY kind of a mismatch (even between the status of a person listed as a green card holder vs U.S. citizen in various databases), the employer and the employee get a "no match" letter, and the employee is then requires to fix the discrepancy within a certain period of time. If the discrepancy is not fixed, the employer may be mandated by law to fire the employee in question.
Basically, you do not want to take these kind of chances. So update your status with the Social Security Administration after the naturalization oath, as you are supposed to, then apply for a U.S. passport and after getting it update your I-9 form, again as you are supposed to.