I think we're in agreement on usd being more tied to real world messiness than the pure theoretical "it cancels out" math view. It's all just trading pair bartering at end of day. But the knee jerk cancel out reasoning is close to reality _because_ USD is so liquid and deep across all trading pairs. That's the point of UoA/money, breaking all trades into a simple linear ordering of one denomination. That you say it's a manipulated or bad yardstick is true, but it's consistently flawed across trading pairs, as liquidity and arb ensure it adapts quickly. That's what they teach you in Econ anyway, I'm sure there are examples where this doesn't hold so well, but my little bit of studying told me arb never last long in modern economies, as there are vultures and bots who make sure of it.
In abnormal times, when capital controls (if that's right term) may take place, then we get to see some action.