Kirk has been established as a history buff. He's interested in Earth's past.
Well, not really. He knows really detailed trivia about 19th century United States (two episodes), but is utterly lost in 20th century United States (three episodes and a movie) or the century in general, unless it's about the Nazis, the pet subject of his old teacher (one episode) and an accordingly biased view.
That's a pretty good indication not only of him being no historian or general history buff, despite being a dedicated hobbyist, but also of him being likely to find his heroes and villains chiefly from the 19th century United States.
Spock has to fill in the details whenever Kirk time travels to the 1930s, the 1960s or the 1980s... In comparison, it's never Kirk who fills in details on one of Earth's bygone eras - except in "Spectre of the Gun".
If Kirk really had hobbies beyond the Wild West, those weren't evident on screen. No doubt he studied military history - it would probably be a mandatory subject at Starfleet. But he doesn't indicate knowledge of past or present politics, art, economics, sports or science. Maybe he is just the strong, silent type, letting his eggheads do the talking despite knowing a trick or two himself. Or maybe he concentrates on what he does and likes best, and only indulges in a single esoteric pursuit on the side.
That said, I second all those comments above that Kirk would have had this particular sort of biased view about the characters in the Excalbian play. Him knowing Green better than the ancients is a good argument; him knowing next to nothing about Kahless but respecting him even less is reasonable; his mind containing a few "contemporary" or "foreign" evils unknown to us is a given.
But the rest is up to the Excalbians. If they get Lincoln out of Kirk's mind, perhaps they then want the next player from a different era and rule out, say, Queen Victoria (either as a top baddie or a top goodie); Green may thematically rule out Hitler; and out of the sixteen or so Klingons that Kirk personally hates a lot, they select the archetype rather than a specific person.
Personally, I don't think any other choice of characters would have benefited the episode, or the Excalbians - the experiment was too alien or ill-conceived for that, and the opportunity to get to know the characters better would not have emerged for any number of rewrites, considering the production realities. But the episode does offer us at least some new material on our heroes and their worldviews and biases, which will have to suffice.
Timo Saloniemi