And the simplest way to win Dom with melee units only is...
-XCOMS - play the game as though you're going for a tech victory, get Mercantilism/Big Ben, go Autocracy for Mobilization. spam XCOMS (get a headstart by building paratroopers, very cheap upgrade) and put a spy or diplomat in every capital for vision. Drop 6 XCOMS per capital, game is won 1-2 turns later.
Haha, I hadn't thought of that strategy! Nice thinking. But do you think 6 XCOMs are enough to take an Information Era city? (I don't know, I've never tried anything so bold, but assuming that they're close to you in tech, my guess would be yes for most cities but no for the capital.)