That's what I've been thinking as well. This might be an unintended consequence if SpaceX is able to reliably deploy the reusable rockets they are drawing today. It might actually require less energy to launch a passenger vehicle above the atmosphere and let it glide/freefall all the way to the destination than it does to push the same vehicle through the atmosphere. I haven't actually done any calculations, though. It would be interesting to see how much energy it would require per passenger to get such a vehicle to a suitable altitude and speed for intercontinental flight. For instance an aircraft powered with combustion engines, with booster rockets attached.
The disadvantage of your solution is the environment impact of such a transportation system. An electricity based solution seems to be much cleaner (especially if we imagine the same kind of traffic as the plane one today).