As has been stated multiple times in this thread and basically any thread involving conversation on the topic, a PoW with a negligible cost (either of time/money/pain-in-the-ass factor) will not impact end users, but will affect LLM scrapers due to the scales involved.

The problem is trying to create a PoW that actually fits that model, is economical to implement, and can't easily be gamed.

But saying "any" seems to imply that it's a theoretical impossibility ("any machine that moves will encounter friction and lose energy to heat conversion, ergo perpetual motion machines are impossible"), when in fact it's a theoretical possibility, just not yet a practical reality.