The only benefit of keeping the card number would be in case you need to go back and look at previous transactions for proof of something, and your bank is unable to find your account with just your name and address.
For example, to provide evidence of business expenses used as a deduction against your income tax, in the event of an audit, or for the purposes of proving you were or were not in a given country or state at a particular point in time. In any case, that information would come from your statements and receipts, not the card itself.
I think for naturalization purposes, you could have to prove that you were not outside of the country for more than 1 year without a re-entry permit, and credit card statements may help with that, but this would normally be in the event that USCIS believed based on some other information that this might be the case.
However usually it is not useful to go back more than 5 years, as under contract law, a dispute has to be raised within 5 years.
Unless you think it would be helpful to get this information at some point in the future, I don't see any benefit.
As for the other information, credit card companies usually tell you to destroy the cards once expired, presumably to prevent them from dealing with the problems associated with someone accidentally using an expired cards.
So in general, the answer would be No.