The main reason the Dairy Supply quota is in place is to stop US dairy producers from dumping dairy into Canada.
That's why the USA has never reached the tarriff limit. The big producers there would just dump 20 million litres at once if they could. They aren't interested in 1 or two.
And if they were able to do that, the Canadian producers would go under. So its kinda simple, the Dairy Supply system is there to protect the Canadian Dairy industry. If it was removed, we would be flooded with cheap, low-quality US milk.
The entire Canadian dairy industry produces less milk than Wisconsin alone. Why does the US need the Canadian market? A: They don't, they just want it anyways.