Do they check if I paid for my carry on?

Flew to San Francisco from DC recently. Saw I had to pay for a carry on if not only one personal item small enough to fit under the seat is allowed.

I did pay then when I was at the gates, they did an announcement about how everyone is allowed only two personal items (under the seat and overhead). Nothing about paid carry on. Didn’t seem they checked who paid and who didn’t either.

So do we need to pay for a carry on?