Absolutely keep it. It's a great card.
Do you drive? Do you take mass transit? If, for example, you have an EZ pass, you can have the refill set to that card and get the 5% on it without carrying it. Or a monthly bus/rail pass. I know that gas is generally one of the holdouts that wants a physical card with you, which would make it annoying in your simple setup. They're also right that in your case downgrading to the BCE, using the CCC for groceries instead, and opening up the 3% in online retail on the BCE might be a "better" setup which earns you more cashback.
Funny thing: your two card setup is exactly what I set my parents up with 3 or 4 years ago! (I was concerned that if something happened to my dad, all their CCs were in his name [primarily for balance transfers initially, and the concept of CC rewards was something he didn't trust at all], and my mom would be kind of screwed, so I had her get those two cards with her as the primary, and my dad as the AU.) They do tend to spend more than the max on groceries yearly, but it's not worth trying to teach them to track it and switch.
Biz - 
Authorized User - 
Debit Cards - 
