I'm sad to report that renting a family bedroom or two joined bedrooms on Amtrak to take a journey on say the California Zephyr didn't pencil out. It is costlier than flying (about $2000 vs $1600 at the low end for both options, resp.) Even if you account for the cost of staying two extra nights at the destination it about breaks even.
With children I don't want to risk the days of travel becoming an ordeal as opposed to hours of flight time. The "digital detox" might quickly go sideways and require hours of screentime pacifiers. Maybe when they are older.
Happily the QM2 actually made financial sense and there would be more room to move about and explore the ship.
I think rail travel makes the most sense in the Acela context the article opened with - routes between cities that take less than a day. For cross-continent travel the time savings of air travel make rail travel a harder case to argue.