I took a quick look. Canada seems to accept around 430k legal immigrants and had another 30-40k illegal crossing in 2022.
The US seems to have admitted 1 million between July 2021 and July 2022 so lets say somewhere around 1 million legal immigrants were accepted in 2022. Illegal crossing were around 2.7 million for 2022.
I take a look at these numbers I scratch my head at your statement. The US has orders of magnitude more illegal crossings. In fact the US average for 1 month is 225k which is almost 6 times as high as the YEARLY average for Canada. The numbers are pretty clear about where they are going. Nothing is stopping those entering the US illegally from entering Canada illegally too. Yet I can't seem to find any numbers that support that idea that even a fraction of the ones entering the US want/try to go to Canada.
https://www.canada.ca/en/immigration-refugees-citizenship/ne...
https://irb.gc.ca/en/statistics/Pages/Irregular-border-cross...
https://www.census.gov/library/stories/2022/12/net-internati....
https://www.nbcnews.com/politics/immigration/migrant-border-...