No transport is free of movement or vibration, cars most especially. Far more get car and air sick than train sick. So unless you're advocating never travelling at all, I'm not sure what point you're making.
From my experience of all, train is probably the most comfortable of the lot, with the best seating, most desk space - you get a proper table and even a mains point. You don't get forced to breathe dry low oxygen air, and avoid the nasty taste of road fumes.
Biggest negative is the relative cost of train compared to all the other forms of transport, which speaks more of relative subsidy than inherent costs.
There might be other reasons to take trains over airplanes, but "so I can comfortably work on it" is a very questionable one.
You can add hours of buffer time if you want (if you're flying to do an organ transplant, maybe that's a good idea); most people can take a 0.5% chance of missing their flight. (I've literally never missed one, though I've been a few minutes away from doing so a couple times, usually because of my own error, once because of unexpectedly long security lines, even for TSA Pre.)
Personally I've never had issue working on trains, and the many friends who use trains regularly seem to do work well enough too.
I haven't experienced any issues with vibration or overwhelming sleepiness and haven't ever heard anyone complain about these things.
The other passengers and background noise are no less distracting than an open plan office, and it could even be much quieter if you have a cabin with just a few other passengers.
A good reliable internet connection is crucial, I agree. I think it should be manageable with proper planning.
Lots of people walk up and down the cars on long trips. You have to walk to get to the dining car, bathroom etc. It's certainly easier and more pleasant to walk and stretch on a train than a plane or a bus.
I've taken that train as well and while it's nice for routes of around that distance, I'm not sure how it would be beneficial if you had to sit on it for days. That wouldn't be much of a sleeper trip.
Also, if we really had bullet trains that could do 200+ MPH, you could have cross-country express trains that take less than 24 hours, so it wouldn't even have to be multiple days.
This isn’t a useful perspective for the majority of people