Team doing the work should do QA so they only produce quality.

But on other hand those people can not often be trusted. As such you need a team that does checks again. Or alternatively they might have misunderstood something and thus produced incorrect system. Or there is some other fault in their thought process or reality. And system operates differently in more real scenario.

QA is actual work. Building the thing is actual work. Each is not "the" work, which is the task of the whole company.

QA perspective and focus is just different from the one of the team building the thing. It's precisely because of their detached perspective that they can do their work properly.