Note that we could already theoretically pack data into separate spatial modes (c.f. [0]), but the problem is in a real fiber, energy will leak from one mode into another, limiting useful signal. Compounding this is that different modes can propagate at different velocities, so you can e.g. have energy leak from mode A to B, travel more slowly for a moment, then back from B to A, which effectively smears your A signal even if you filter on the ends. This is why single mode fiber (i.e. fiber thin enough that only the single 00 mode fits) is used for high data rates/long distances. The same thing can happen with polarization modes, which you can't eliminate by just making your fiber smaller, so IIRC they are actually the enemy. So there are real engineering challenges to actually make extra channels be useful rather than harmful (this is all recollection of uni courses 15 years ago, but it seems single mode fiber has only become more popular, so I suppose it's still an issue).
[0] https://en.wikipedia.org/wiki/File:Intensity_profiles_of_Lag...