And solve the trivial engineering task of reducing all friction and air resistance to zero.

Well shit, anyone can do that. Just put a little WD40 on it

You build your track dead straight - like, not conforming to the surface direct through the crust straight. Now the train accelerates downhill for the first half of the journey, and decelerates uphill for the second, neatly coming to a stop at the destination. Oddly enough, in the spherical cow universe where you build this, all the maths cancels such that you get a constant travel time regardless of the start and end locations. On earth it's about 40 minutes

You need energy to decelerate, though.

you could conceivably get on and off the train with shuttle "station" trains that travel on parallel tracks to catch up with the main train

🤔 A vacuum tube maglev would do the trick.

Actually Isaac Arthur talks about something like that on his channel. An Orbital Ring, he calls it.

I swear I came up with the iphone... my design was a triple flip phone, screen up top, keypad in the middle and an ipod wheel down bottom

Just tie it to the moon.

I think in that case, the earth would just depart the location of the train, leaving it drifting in space.

No, the problem is not gravity, is that the train attached to earth has velocity dictated by the Earth movements, and keeps it because of inertia. In your theoretical experiment, the train would be launched on space at constant velocity.

The problem isn't gravity, it's friction. The train would functionally be in orbit. The reason why things can't be in orbit at ground level is not because of gravity but because of friction (incl. air resistance).

If you eliminated friction (vacuum tube, frictionless surface, etc.) you could indeed have the train moving without any additional energy after getting it up to speed (and if you get it up to orbital speeds, the frictionless surface isn't even necessary). However, this isn't really practical (obviously).

If there is a nugget of a good idea in here, it's a train that never needs to accelerate or decelerate, just maintain a constant speed. Much of the energy of a train is lost in the stop-and-start.