Just accept them for what they are. I enjoy playing Terra maps but agree that settling the secondary continent is usually counterproductive, but that isn't the sole purpose. There are many unusual characteristics of Terra maps that make them interesting to play -
1.) First off, there are three main map components to a terra map, not 2 (Old World and New World). There's the continent where all civs start, an archipelago off the Old World, and the New World.
2.) What I find to be the defining characteristic of terra maps is the early game real estate situation. The terra map as a whole is larger than a regular map, but the landmass that all 8 civs (standard size) start on is considerably smaller than a pangaea, which makes for some interesting dynamics:
-it's a frickin' powderkeg! All the AI's borders are meeting earlier, all the areas that AI's want to expand to are already occupied by someone else. So they are constantly warring with each other and more importantly, are unusually susceptible to war bribes and "lets war against" proposals.
-at moderate and higher difficulty levels, you're probably only going to be able to settle one city, maybe two besides your capital, so how are you going to deal with this? Two or three cities with Tradition can be very effective, especially for Aztec, Babylon or Korea. Another option would be to take advantage of the AI's lack of ability to expand off-continent and utilize the archipelago that is off of the Old World, a particularly good option for Japan, Carthage, and of course Indonesia. You can also respond to the early real estate situation by force, a great option for the early game siege guys, Assyria and the Huns.
3.)City states. At least 2/3 of the city states are on the New World and the AI seems to be less interested in getting astronomy (probably because they're too busy with the land wars with each other.) Which means that you can have a large number of, even the majority of the city states and have no one else competing with you for their influence.
Finally, the other maps don't have any huge mapscript-based bonuses either! I think some of the disappointment many players feel towards Terra map stems from the illusion that there should be some massive bonus achieved if you're the first civ to find the New World, partly because it's a defining characteristic of the map and partly because of real world history. But the fact is there is no big bonus, the closest thing is sole interaction with a bunch of CSs. But the other maps don't have any big bonus for "you cracked the map-script miniquest" either. There's no bonus on pangaea maps for unveiling all the pangaea tiles and no circumnavigation bonus for continents/archipelago maps.