Very good!
The “[sic]” is not required. That’s how they wrote back then.
in·ci·dent/ˈinsidənt/
Noun: An event or occurrence: "several amusing incidents".
Adjective: Liable to happen because of; resulting from: "the changes incident to economic development".
It is a misfortune [sic] incident to republican government,
Whoever thought that was a mistake probably thought the word needed to be “incidental” to be used as an adjective. Perfectly ok in Madison’s time, though.
I think the editor thought he meant to write “misfortunate”. You are correct however and Madison was correct.
It is ironic that the same person who wrote this later helped Jefferson create what became the Party of Destruction which is destroying our nation.
It is a misfortune [sic] incident to republican government, that those who administer it may forget their obligations to their constituents, and prove unfaithful to their important trust.
I fail to see how the construct is faulty, and I cannot help but admire the efficient yet forceful expression of eloquent thought.