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.