There's a very big assumption in your claim, which is that immigration is balanced among 'social classes', skills, jobs,etc. In that case, indeed overall demand grows along with overall supply. Australia has an immigration system aimed at achieving that.

Things do not work out so great if immigration isn't balanced.

In the UK there has been a huge influx of unskilled or low skilled workers from Eastern Europe that has put a big dampener on wages at the low end of the spectrum.

One of the reasons the UK has a productivity issue is that cheap labour.

The papers I linked are empirical evidence, not assumptions. There’s two specifically on the UK that find no evidence of this.

They also find that skilled immigration systems don’t always work, because all immigrants tend to be unusually highly educated anyway, but also significantly downskill the jobs they choose after arriving. So you’d expect them to always compete with low end natives, but in fact they don’t because they mainly compete with other immigrants instead. And “compete” isn’t how labor works anyway, since all workers are also customers.

"Negative effect at low-end of spectrum", which is what I wrote...

> because all immigrants tend to be unusually highly educated anyway

That's obviously not true.