I went to boarding school in Toronto, not one of the ones you listed but same idea.
You are right that about 25-30% of students go to US (or UK) schools. But it isn’t because of rejection from top US schools, it’s because Canadians aren’t conditioned to pay a fortune for university. So most Canadian boarding school parents are only paying for the very tippy top US colleges. And some won’t do that.
I went to an elite LAC and everyone thought I was nuts. My parents grew up in the States so they encouraged it, but the only kids in my class who went to the US went to ivies or one went to play hockey at Notre Dame.
As for preparation for US schools. I graduated from high school in 1995 so things have likely changed. But I was a better writer, a poorer math student, and way more mature than my American counterparts.