Up until the US Civil war, it was the universal practice to bury the dead close to the battlefield.
With the invention of embalming, many of the civil war dead were shipped back to their homes for burial.
US war dead in the World Wars were buried near the battlefield, because transportation of the remains would have taken up valuable transport.
During Vietnam, transport was not an issue, and the dead were repatriated.
These remains are not interred, so shipping them back, and interring them in a German war cemetery would seem like the logical thing to do, the symbolism of the homecoming after so many years, even for the remains of the unknown, might be a comfort for those whose family members never returned.
I am certain that if unburied US remains were found, they would be returned to the US.
You might be right about burial near the field of battle as a cultural thing, where US culture is more attuned to homecoming.

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“ The subjects of every state ought to contribute towards the support of the government, as nearly as possible, in proportion to their respective abilities; that is, in proportion to the revenue which they respectively enjoy under the protection of the state.”

Adam Smith , The Wealth of Nations 1776

"We have always known that heedless self-interest was bad morals; we know now that it is bad economics"
FDR's second Inaugural Address