The Queen is a symbol of the UK's terrible past just as much as Barack Obama is a symbol of the USA's terrible past. In fact, the Queen was a figurehead and had zero authority over any decisions that the British government made.
Nobody chooses to be born into their specific circumstances. Barack Obama overcame all of the circumstances of his birth and became more powerful than the Queen, who gained her position by birthright.
Scoffing at someone for benefiting from the circumstances of their birth is an outdated, pessimistic and cynical worldview in my opinion. It's out of touch with a world where Barack Obama and Rishi Sunak and Leo Varadkar are world leaders. Everyone is free to keep having those views though, I just don't relate at all.
Is this to imply that a country has nothing to gain by going to war with another country? Obviously not, war costs billions, and the US wasn't directly (or arguably indirectly) under threat from vietnam, so there wasn't any reason to engage in war unless they had something to gain (or fear losing, which seems just as bad).
Going by the logic that the US had something to gain in engaging with war in Vietnam, or any of the other many places they've done so, it stands to reason that future presidents would benefit from it. Maybe not in extracted wealth, but to say anything goes unless its directly earning money from it seems a bit odd.