That's a very interesting theory.

Presuming that people should be able to survive the journey, whatever structure it is you're considering for a mag-lev launch would have to be absolutely MASSIVE (they have solved the problem in your above picture with an infinitely long cantilever beam, nice!). The scale of this project could potentially dwarf the LHC, and certainly in cost, as human life enters the equation. The only place worth building such a thing would be so far removed from active tectonic zones that selecting a candidate site would take years, geopolitics aside (continental US doesn't look good for a ~100 year investment, northern Alaska looks OK though - EDIT: sorry, the best places in the US are the northern great plains, Texas, and Florida). They might even finance strategically dyanmite'ing nearby fault lines as a precaution.

The main problem is that if you were to shoot out of an evacuated tube anywhere close to the Earth's surface near escape velocity, that's about like hitting the surface of the ocean falling at terminal velocity. You'll have to make sure the shock of hitting atmosphere doesn't kill your passengers. So put a very long tapering nose to ease the transition? That's mass, and it's gonna cost you a shitton of energy to accelerate. So build it high and have a gradually increasing pressure as the vessel ascends in the tube until you exit the tube? That's gonna make the Burj Khalifa look like child's play.

All other speculations aside, the most obvious design feature is to have the thing be totally vertical. How much of the structure would be above the ground vs. subsurface is the only debate in that vein.

Not sayin' you're wrong, but it's a huge challenge with today's capabilities.