He was elected by a rump plurality, sort of like Bill Clinton. Elections for the Presidency should require at least a majority. With pluralities, you can elect a man that the majority hates.
Also, the right to independence would not have changed had George III been elected. It's not about how a government is constituted that matters, it is the "consent of the governed" that is the sole requirement for governmental legitimacy.
Does “consent of the governed” mean “consent of every community”? Can a town choose to become independent? Can a county?
The solution to the election of Lincoln was to fight him in Congress and elect someone else in 1864. Lincoln wasn’t going to abolish slavery.
BTW: As much as I disliked Bill Clinton, he was the President. Didn’t matter that he didn’t get more than 50% of the vote. People have to factor that in WHEN they vote.