Some US airlines will gate check carry-on luggage, either when they run out of overhead compartment space or when some bags are too large. In theory, would it be possible to bring a large suitcase (one that a sane person would check) to the gate, then have it gate checked there for free?
Bags which exceed the allowed size (or number, or weight) for carry-on are not gate-checked for free. You are charged a fee for this, which is usually more expensive than if you had paid for it in advance.
Items which are gate-checked for free are those within the allowance which won’t fit in the cabin due to lack of space or because the aircraft has smaller than usual overhead bins.
In addition, past a certain size, larger items won’t be able to go through security as they don’t fit in the scanners, so you wouldn’t even reach the gate.
There are a few exceptions for some specific items (especially larger musical instruments), but those are quite limited and often have specific rules (like booking an extra seat for your cello for instance). They vary from airline to airline.