https://www.bankofcanada.ca/wp-content/uploads/2023/12/remarks-2023-12-07.pdf

The Bank of Canada says they do drive up home prices, which has an effect on inflation.

The "labor shortage" is the Phillips curve, caused by QE, which caused the 8% inflation we experienced after Covid. Its not a real shortage, and the increased economic activity is temporary, as the BoC then raised rates to cool the overheated economy.

So you're idea that you're simply filling up job vacancies because our economy is strong is wrong, what youre actually doing is preventing wage pressures from correcting the wealth inequality the Bank of Canada's QE caused. This is straight from a BoC publication as well that explains how wage pressure are a natural equalization after a bout of inflation, reversing this via mass immigration is bad for non-asset holders, which is why wealth inequality between renters and home owners increased so dramatically.

But thats easily seen by looking at the growing food bank usage, growing homelessness, growing wealth inequality, and reports like this:

https://nationalpost.com/opinion/secret-rcmp-report-warns-canadians-may-revolt-once-they-realize-how-broke-they-are

If you were around in the 70s and 80s you'd likely be one of the people blaming unions for "causing inflation", and telling them they needed to accept lower wages.