Hamilton was but one of many. If you have some free time, I recommend diving into the convention notes found at the library of congress. It’s quite fascinating learning what the framers really thought during the construction of the Constitution.
Either way, Hamilton got his wish. All but 1 president had royal blood tracing back to the English crown on his father’s side, and that president was none other than Martin Van Buren. Even though his direct paternal bloodline traced back to the Dutch crown, his grandfather on his mother’s side was linked to William the Conqueror. Ironic? Coincidence? Or design. You choose.
With the Declaration of Independence, these colonies declared "That these United Colonies are, and of Right ought to be Free and Independent States" (each on equal footing with the state of England, the state of France, the state of Spain, etc.).
The Constitutional Convention created a union (a compact, or contract) among these sovereign free and independent states, with specific enumerated powers delegated to that central created entity (and most of those delegated tasks pertaining to foreign affairs). The federal government is not a sovereign entity. The states and the people are.
Therefore, the whole discussion about royal bloodlines in the federal government is moot.