I'm very familiar with the scope of the admissions challenge and it's not really an issue of number of applicants. Most universities already have an understanding of different high schools (though often biased to wealthier communities). As for Canada, specific programs at Canadian schools can be quite selective - for example EngSci at the University of Toronto has a ~10% admission rate. Other programs are more like state schools in the US. Most elite schools in the US are still pretty regional heavy. For example 35% of Stanford undergrads are from CA and something like 30-40% of Harvard undergrads are from New England and the mid-atlantic.

Can confirm, some programs and unis are very selective with very low acceptance rates but the average student doesn’t usually have too much trouble getting into a relatively good program without having to do standardized tests