I don’t see how he would know more. Note that Hamilton had a poor attendance record at the Constitutional Convention imo.
In fact, James Madison, Hamilton’s foe, logged the most complete record of the ConCon debates imo.
"One of the reasons the Democrats reauthorized the National Bank was the inability to fund the War of 1812."
The temporary national bank signed into law by Pres. Madison was arguably a martial law bank. If the states want a peacetime federal national bank then there’s nothing from stopping them from appropriately amending the Constitution.
"In every event, I would rather construe so narrowly as to oblige the nation to amend, and thus declare what powers they would agree to yield, than too broadly, and indeed, so broadly as to enable the executive and the Senate to do things which the Constitution forbids.” —Thomas Jefferson: The Anas, 1793.
Regarding centuries old state versus constitutionally limited federal power power struggles concerning the “necessary and proper” clause (1.8.18), consider this insight.
"It is easier to get forgiveness than it is to receive permission." —Rear Admiral Grace Murray Hopper, U.S. Navy's Chips Ahoy magazine (July 1986)
Hamilton was an ally of Madison when the CC was held, only after TJ’s return to the country did he fall off the wagon. H did not have to attend every session to be aware of what was going on and why. He explained what it meant in the Federalist. He also gave an all day speech unlike anyone else.
H. was a member of the Committee on Style which did the actual writing so was well aware of what was meant and what was not.
Jefferson repeatedly showed no real understanding of the constitution so I don’t care what he says. Hamilton is the ultimate authority and explained clearly what was constitutional and what is not.
A bank was clearly constitutional on several grounds. George Washington (who DID attend every session) acted promptly after receiving Hamilton’s opinion, Jefferson’s was so transparent, short-sighted and flimsy he had little choice.
The Second National Bank was established under a Jeffersonian Congress which painfully realized he was wrong in his opposition. It was chartered for 20 yrs and functioned until Jackson could destroy it (and much of the national economy.)
If it was a military operation that clearly shows both its necessity and its constitutionality. Its use in funding war was explicitly pointed out by H in his Essay. His initial belief was that it would be to costly for the Empire to fight the US but later realized that the Bank of England allowed it to handle those costs. Hence, the clearly demonstrated utility and the need for one of its own.