I'd actually argue that Lincoln would fit better as a Rider, since that seems to be the most fitting Class for leaders of men. Admittedly a lot of said leaders are of the military variety, but not all of them, and Lincoln was a wartime president.
The main issue I have with Lincoln as Rider is that he was never really a
soldier, even if he was a wartime President; even as a militiaman, he was considered competent, and persuasive enough to be elected captain, but he never actually saw battle. I'd still call it a better fit than Caster or any of the other standard classes, but his martial leadership was more down to his generals, with the real genius of his administration being his ability to keep the rest of the government working to maintain the war effort.
I've also seen someone also propose a Nightingale/Spartacus hybrid sort of Berserker focused on slavery, though frankly Lincoln is still a poor fit for that - Lincoln was a moderate abolitionist, and viewed it more as a political than ideological issue. (If Civil War alt-history wasn't played to death, I'd love to see a POD where Lincoln decided to go forward with recruiting Garibaldi.)
The other issue with Rider is that there's many better-suited Presidents for it; Grant being the obvious point of comparison, but even outside of Civil War specific situations, there'd be little reason to summon Lincoln as a Rider versus Washington, Teddy Roosevelt, or (much as I hate the man) Jackson. Hell, maybe even Eisenhower, if the Grail War were in the right part of Europe.
(My
biggest bias pick for a Rider from the Americas, though, would be L'Ouverture.)