It does run on lower frequencies. That has NO relation to throughput at all, however. What does have a relation to throughput is channel width, air interface technology, error rate, channel load, etc.

There is the potential to make a terrible air to ground network, a terrible air to satellite network, or a mediocre network with either setup. Great is, sadly, rather infeasible.

Gogo uses Qualcomm CDMA, with narrow channels and low system bandwidth. There have been discussions on adapting LTE for air to ground, with wide enough channels and a good network design this could have a lot of potential.

Lower frequencies? Almost irrelevant (there are network design implications, thus the almost)

I probably oversimplified it, but lower frequencies do make it more difficult to get the necessary spectrum to make things fast for everyone. The main point is that connectivity is almost (if not already) at the point where real-time authorization at 35,000 feet is feasible.