It’s not important whether the train has a WiFi router or not. What is important is what the WiFi router connects to. I don’t know what is common on European trains, but in the US they connect to whatever cell–phone network is closest. That is ok in urban areas, but in the US there are wide stretches of countryside where nobody lives. Somehow the phone companies never end up building cell towers in the middle of the deserts or on top of the Rockies. The train could easily be 50 or a 100 miles away from the nearest cell–phone network at any given time.
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