If they were actually accepting all applications that meet the criteria, that would make first come first serve more fair, but there are quotas so they have to reject N-1 applications regardless of their application.

Lottery systems are generally considered fairer than first come first serve because they don't advantage people who apply early. Especially in an immigration-related process where circumstances are likely to dictate when you can apply, not everyone will have an opportunity to 'get in early'.

If you have a way to make the process simultaneously non-random, fair, and not have a cap (which I personally would probably be fine with eliminating but is presumably a non-starter for various political reasons), I'm sure some people would love to hear about it.

Why is that wrong? How do you propose to select to pick who gets in and who doesn’t?

The other options are to let everybody in or to suppose you already know the right criteria for who'd be the "best" immigrants. Hint: you don't.

Genuinely random selection averts loads of really nasty problems in a system where you need to pick things even though humans tend to be sure some other approach would work better.

I would imagine it's because there are a limited number of people that Canadians will allow to immigrate into their county?

While it does seem wrong and silly, isn't a completely random lottery explicitly fair? No one involved is privileged by any metric (unless you believe in supernatural luck).

Unfair to whom? That is going to be relative.

Its still better than using the place of birth as a determining factor.

"The Liberals introduced a lottery in 2017 in an effort to make the system fairer – previously, applications were accepted on a first-come, first-served basis. The program receives roughly 100,000 applications each year and selects 10,000"