I have the same Barclays, rolled over from US Air. They just sent the new one in the mail. I’m about to throw it in the drawer. I’ll pay the fee just to have the credit available.
I also have the Citi World Elite. We use it for everything personal. It is great when abroad because you can easily set the travel settings. Admirals Club Access is fantastic. The first time we took my in-laws in, my FIL said “Are we allowed in here?” It really eases the craziness of the airport for us.
So to answer your question with a question, why shut off either?