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).
For varying hardnesses of vacuum, you can find a partial vaccum of 4 psi at 30,000 feet.
Which is enough to drop drag a lot, and still maintain lift in, say, commercially viable air transportation vehicles.
Lowest costs I've seen to LEO are about $1,000/lb. Suborbital flight isn't much lower than that, and we're still looking at something on the order of $10k - $1m per passenger at rates like that. Affordable to some, but (considering you've likely got a baggage, life support, and related allowance) pretty pricey all the same.
$10k is comparable to Concorde, as I recall. I consider that a very optimistic estimate.
I can't imagine it'd be more expensive than tunneling 3000 miles under an ocean.