Because the triangles that make up the globe (and any other 3D surface, really) hopefully are way too small to use them as tiles. Optimally, the number of triangles making up the globe adjust to your hardware capabilities, ie dynamic LOD. And of course, the globe shouldn't be a perfect globe, mountain ranges and such deviate from it, just as the real Earth - you can't leave those out since they are critical to the game. Of course, you can have a grid of additional overlay set of triangles that are based on the visual geometry but a lot larger. (Setting the game grid to the geometry triangles would be similar to equating the grid on a 2D game with the pixels that make up everything.)
Overall, I like the idea of a gridless Civilisation a lot, though, I think you can convert all game mechanics without too much loss and it would be both better looking and more realistic. On the other hand, you'd probably have to add or change mechanics to make the gridless element add anything to the gameplay, and depending on how you do it it might be more complicated than the grid abstraction.
Ever since, in Elite: Frontiers, I lifted off and was able to fly my ship through the atmosphere slowly recognizing the curvature of the planet and then seeing the planet's continents and eventually the globe become smaller as I left it, I'm hooked at displaying globes in games. To me it was a pretty mindblowing experience - and that's with the graphics capabilities of, what, a 386? Today we could draw lush landscapes, oceans, woods, farms, industry, pollution, an atmoshpere, fairly stunning. Maybe there could be a projection to a flat Earth available - like the ones you get on a real map. Actually, that could be the only available view until your civilisation is aware of the global nature of their planet...