Maybe it's obvious, but you left out subsidized. US dairy production is extremely subsidized compared to Canada's. It's not in any sense "free trade". The subsidies would allow the US dairy industry to destroy Canada's (it might even without the subsidies, but the subsidies guarantee it). Once the local industry was destroyed, the US producers/government would be free to increase the price. No country wants that, which is why things like staple foods are subsidized and tariff-protected anywhere in the world where not doing so would give a large neighbor/bloc leverage over them.
That's just a convenient talking point for our government. The model in Canada is effectively a regressive tax on consumers in the checkout line. It conveniently allows for our government to talk about how they don't subsidize farmers, and have a clean budget on that front, but I would prefer to see a model that was actually funded by government taxes such that it could be a progressive tax born more by wealthier Canadians rather than lower income ones being hit hardest.
I also have doubts that our current model is the best way of achieving the goals we had in mind when the programs were created in the 1970s. I know the error bars are quite sizeable, and it's not quite apples to apples, but recent studies that suggest our supply chain management in dairy, eggs, and poultry, costs approximately $244pp per year in higher costs. That's over $10billion per annum Canada wide, equivalent to 2% of the federal budget! I have been discussing this with someone in another thread for days, and the more I look into it, the more I feel like we really need to take another look at the implementation of this program. Dollar amount breaks my brain.