I've got a jar too, but it definitely doesn't fill up at anywhere near the rate yours does. My pay is direct deposited and every place I shop will take a card. I could either go to the ATM to get cash, use it to pay for things when I don't have to, collect these small amounts of change, and take it all back to the bank eventually, or I could just not bother with any of these things.
I almost never have cash on me. It's debit or credit always. Here's my thought process on paying with cash. If I buy something that costs, say $4.55, and I hand over a $5 dollar bill, that item has really just cost me $5.00 because what am I realistically going to do with the 45 cents in change?