Apparently the broadband out there is great. The issue isn't lack of satellites or speed.
The issue is that when you have a Merlin 1D (or 3) firing directly at a mobile platform, it's going to shake violently. And when you have sensitive equipment on that platform shaking, you're going to have a satellite misalignment and signal cut outs while the lock is reacquired.
Considering this is a pretty unique scenario (I would imagine 99% of satellite internet connections don't have rockets landing on them), I doubt it's a high priority to resolve somehow.
I did see something upright though, so who knows.
Meanwhile, for anyone looking for one of the most epic moments: https://youtu.be/L0bMeDj76ig?t=29m28s