Both facts may be true without the causal link being present.
Establishing the US as the global reserve currency had little if anything to do with where gold was stored, and far more to do with US economic and military power generally in the post-war era.
That’s incorrect. It had a lot to do with it because it represented the fact that Europe’s governments had little to no wealth after WW2 while the US had it all (thus economic and military dominance).
True, but gold is (and especially was) a store of wealth, into which "produce and labor of the nation" had been converted over time by European nations