Theoretical max height for a building using conventional skyscraper techniques is 11 miles, at which point it's ridiculously expensive. Someone at JPL did a work up of using columns made out of ultra pressurized boron balloon tanks, and found that 100km is actually possible, though also ridiculously expensive.

A rocket would have to undergo some fierce acceleration to gain any useful speed over that distance.

To convert a Falcon 1st stage into a cheat-SSTO, all you need to do is to lighten it a bit and give it a bit of a boost. Such is the nasty nature of the rocket equation. You have to accelerate the fuel you need to accelerate the fuel. So by "cheating" with accelerating the fully loaded rocket, you save a lot of fuel weight for the same final delta-v. Due to the same nasty mathematics, this translates to a tiny payload, of course.

I suspect economics plays a big role here. I suspect it is cheaper to launch multistage rockets than to build a mass driver long / tall enough to be useful.

Yadda yadda. Yes, this comes up in just about every discussion like this. It's just neat to think about what else you could do with a Falcon 1st stage. I mean, would you turn down a single stage vehicle you could take into orbit? It would make an extravagant billionaire's toy.

Actually, this general sort of scheme does have a practical use. Modify a methane-oxygen fueled 1st stage so that it could make it to a somewhat higher orbit, but still have payload for a docking and remote maneuvering system. Then have the empty tanks dock with each other to create a space station with tons of internal space. You couldn't do this with the Falcon 9, as it uses RP-1, but methane and oxygen would just boil off into vacuum.