Why is Amtrak’s WiFi so bad?

The big one is that planes have line-of-sight to satellites or ground-based stations. I don't know the specifics of Amtrak's system, but trains sometimes use satellite on remote routes. Trees or buildings or bridges get in the way sometimes.

More often the mobile network is used. Cellular technology wasn't really designed with high-speed vehicles in mind, though 3G and 4G systems at least make it possible up to couple hundred mph generally. Back in the 1G/2G days it was common for calls to drop if you moved at even moderate speed.

At the radio level, the Doppler shift of a moving vehicle affects both OFDM and TDMA style codings, effectively lowering the signal-to-noise ratio, forcing lower coding rates. When the train gets going really fast, the time to find, and hand over between cells becomes significant. It can happen up to like a dozen times a minute. Sometimes nothing is found in time during a dead spot and packets hang or drop.

I'm often amazed it works at all.

Topography gets in the way. Planes have a clear view of cell towers on the ground, satellites, etc. Planes never go through tunnels.

With trains usually mobile-networks are used. And trains often travel through areas with on average less demand so weaker or no coverage. Also a train can cause pretty high peak on load on cell for relatively short time periods at time due to high number of passengers present in single train.