I think every airline who gives you a free carry-on will check it at the gate for you for free. In fact, they’ll often beg you to do so. But at that point you’re losing the benefits of carry-on baggage like access to your stuff during layovers, getting to skip baggage claim, and no chance for them to lose your stuff.
At least for Delta, they’ll book your carry-on for free. So there’s that.
I think every airline who gives you a free carry-on will check it at the gate for you for free. In fact, they’ll often beg you to do so. But at that point you’re losing the benefits of carry-on baggage like access to your stuff during layovers, getting to skip baggage claim, and no chance for them to lose your stuff.