Keeping your social security card stored in a safe place does make better sense than carrying it around in a wallet or purse, but the problem is that many places ask to copy your driver's license and social security card as proof of identification. I've been asked to produce both items when filling out a job application, waiting in a doctor's office or applying for any kind of benefit.
It's hard to know when to take your social security card with you and when to leave it at home. You're not supposed to laminate the card, either, so it is bound to wear out over a few years. I think it would be good to print those things out on a more durable material if they're meant to last the lifetime of the holder.
I remember when most driver's licenses had the driver's social security number printed on them. I believe it's optional now, but most people ask that it not be shown. It seems to me that the current number system is going to run out eventually, so we may all get issued a different kind of number in the future, maybe with more numbers or letters to avoid duplication.