You know as little about Hamilton and the constitution as you do about political science it appears.
The Constitution SPECIFICALLY allowed Hamilton to be president and he would have been one of the greatest there is no doubt.
Hamilton arrived in the colonies at the end of 1772. Hence, he was eligible to be president as Article II, Section 1, paragraph 6 says. “No person except a Natural Born Citizen, OR a citizen of the United States at the time of the Adoption of this Constitution, shall be eligible to the Office of President; (this qualifies Hamilton as it did other Founders; neither shall any person be eligible to that Office who shall not have attained to the Age of thirty five years, and been fourteen Years a Resident within the United States. (Hamilton was here for fourteen years.) The Natural Born requirement did not affect the eligiblity of the Founding generation.
When the ignorant criticize one of our greatest Revolutionary heroes, Alexander Hamilton, they are criticizing George Washington who loved the man and supported even after the Jeffersonian scum tried to destroy him. He was the greatest political writer of his generation.
Burr was a typical Democrat crook aligned with the model of corruption - NYC’s Tammaney Hall, the vote stealing sink of thievery. He shot Hamilton because Hamilton had wrecked his political career stopping him from becoming president in 1800 and governor of NY in 1804.
It is particularly gratifying to watch as Jefferson viciously turned on the man who had put him in the White House and proceeded to tyrannically destroy him. Read about the Trial of Aaron Burr if you want to see the real Jefferson.
Hamilton’s death (voluntary from all evidence) also destroyed the secession movement growing in NE which Burr would have brought NY state into had he become governor splitting the union.
There is some debate about the eligiblity clause as relates to Hamilton, because of his origin on Nevis.
I do not hold Hamilton in high regard, having read much about him. Maria Reynolds and paying blackmail jumps to mind.
/johnny