Fact: The USD has large foreign demand which does not exist for other currencies.

Fact: If more currency is demanded, it strengthens the currency in a relative sense.

Fact: Therefore the USD is stronger than it would be otherwise, considering only local demand.

Your whole counterargument seems to be based on a misunderstanding of real vs nominal. To say 1 Euro > 1 USD means people in Euro earning countries have higher purchasing power is simply wrong. All currency values are nominal.

Fact: If USD money supply doubled overnight and all holders got 2x the amount and wages/prices adjusted automatically, the Euro would appreciate 2x against the dollar.

Fact: That does not mean Euro earning citizens have higher purchasing power. It's an entirely nominal change. 1 hour of labor in USD terms earns the same in purchasing power, regardless of the face value of currency. Same concept as a stock split

Fact: If Euro became the reserve currency tomorrow, Euro-holders would have more purchasing power due to foreign demand making each unit of currency more valuable in a relative sense than it was previously.

Fact: If USD lost reserve currency status, it would weaken relative to other currencies.

None of these are disputed, but you can believe whatever you want.