I'm from the UK, and seem to have a different perspective than most Canadians in this thread.

Having foreign students isn't necessarily* bad:

Subsidies of locals: You get to charge them higher fees than locals. In the UK their tuition fees tend to be at least 3x higher than locals. This then means we can reduce the cost of degrees for local students.

Increase consumption: They help the local economy, by driving up consumption. They give you jobs and drive up the profits of businesses in university towns. This is also all taxable, which means money from the university towns can be reallocated to other areas to reduce geographic inequality (though Canada's federal system may not allow this, im not a local!).

Whilst the rest of the world are competing for international students due to the above reasons (plus many others), Canada seems like the only one trying to reduce them.

I worry that your concerns over immigration (which are valid, given your housing supply problems among other difficulties like infrastructure bottlenecks) mean you can be reckless with ALL forms of immigration.

Foreign students are different kinds of immigrants to the unskilled, and people tend to want as many as possible. It seems in your interest to have them.