That is not quite correct and an oversimplification of how modern stoves work. Some stove manuals are better than others at explaining this. There is a balance between a long hot burn and a bright flaming fire. Running with the primary air open wide will make for a cooler fire in the firebox and a much hotter flue because that is where the secondary burn will be trying to happen. This can be bad for the connector pipe if it is staying over it's sustained ULC S641 temperature rating. For better stovetop heat you want the secondary burn concentrated in the stove itself.