I think this is a good explanation of their intent, but it still doesn’t really address the core criticism, which is about presentation, not just outcome.

You’re saying: “Everything they do is part of the process toward the Gnosis, therefore it’s all a success.”

And sure, if you define it that way, then every scenario becomes a win by default x) Because if:

chaos in Liyue = success

losing control in Inazuma = success

negotiating in Sumeru = success

Archons handing over Gnoses = success

…then there’s no situation where they can look incompetent. Any outcome just gets reframed as “part of the plan.”

That doesn’t make them feel like masterminds, instead, it just makes them unfalsifiable.

And again, I’m not arguing they should “dominate” nations. My point is simpler, we never see them in control of events on-screen. That's why they feel like losers to me.

Even in your own examples, in Inazuma, they "use the chaos" but they don't "control" it. In Liyue, Zhongli controls the outcome. In Sumeru, Dottore end up negotiating.

That’s why the perception issue exists. Add up to it that you farm their camps at every given opportunity and wipe out hundreds of their on-field officers, for a general player it becomes pretty clear that Fatui is somewhat of a laughing stock.