Hrmmm, bit bothered by this... 1620 sounds very much like an arbitrary limit, simply based on the fact that that's the time it took the Tokugawa to unite Japan. In other words, if you're doing it slower, then you won't get the chance to finish, even though there's no good reason why.
In that sense, all of our games (and many other games) end arbitrary. We could of course set the end date to 1800 but that would mean we release a game promising game-play up to that date and the game does not feature that. The game mechanics devised for this game fit the era that we chose. However, should you personally want to play a longer game, it's very easy to do, just change one date in the settings file.