Amtrak actually tested the system on the AutoTrain and it failed miserably because in far too many places the cellular data signals simply weren't strong enough, if they existed at all, to service the train.
Ding ding ding. When the train happens to be within a mile or two of I-95 (or possibly the old U.S. routes that I-95 runs parallel to), there could be signal. But in a lot of places, the ex-ACL track runs through the middle of swamps or farmland. The constant drop-outs take a while to recover from.
Well that is indeed part of the problem. Another part of the issue is that in many places, while the cellular modems are picking up data signals, they're simply not strong enough.
When I travel the AT and Silvers, I can usually manage to stay on line for much of the run; at least when I'm not asleep. However, I'm often making do with only 1 or maybe 2 bars worth of signal on my phone. That's OK for just one person, if a bit slow. But try splitting that weak signal up for 100 users and the WiFi quickly becomes totally useless.
Along the NEC, the modems largely maintain 4 bars or more of signal strength, and the system automatically switches to the service providers that currently have the strongest signal to further improve overall performance. But when every provider is only providing 1 bar of strength, switching doesn't help much.