You either lose energy to gravity during the launch or while in the air. Either way you lose that energy, it really doesn't matter when.

Rockets turn sideways because when you're in orbit, you're moving sideways.

You're right, but look up gravity drag. Every second you're standing on your boosters you're wasting fuel. Imagine wearing a jetpack and wasting all your fuel hovering an inch off the ground. If you turn horizontal the thrust is invested rather than spent, but first you have to build enough speed to not crash.

Actually, once you get to a high enough altitude, it doesn't take that much fuel to maintain your speed. The "Pop-up" trajectory (first stage up, 2nd stage forwards) is one that's actually practical and has been proposed for TSTO.

Better yet - tunnel it underground.

Nah. You'd be better off building it up the side of a mountain (or mountain range). You want the air to be as thin as possible when the projectile hits it going mach 25 (or whatever, depending on where it's going).

tunnel can be environmentally controlled, which is good to reduce the possibility of combustion (argon gas). The force against the rails can be mitigated by the constraints of the earth it self at tremendous pressures. The exit can be out of the side of the mountain, its somewhat arbitrary. More importantly the tunnel/launch tube should be at/near the equator.

And yes, since the first half of the tunnel is sloping downwards you are using a large fraction of g to accelerate the slug/projectile, thus reducing the power requirements.

Its an engineering problem, not a physics problem.

Unfortunately a project of this scale is beyond the largest organizations that exist today, nation-states. Maybe later?

When the day comes for the need of a super-structure to be built in orbit, this technology will likely be used. This or a space elevator. Getting far enough away from our own gravity well will free us from this rock.

It's feasible to build a structure about 10 miles high using even conventional construction techniques. (Which would allow for orbital velocities at under 500 gravities.) Some folks at JPL have determined that aircraft building materials make 60 mile high structures possible.

I think our government should build such a launch accelerator in the desert somewhere. (Tilted at 45 degrees or so, to get a cargo drone out of the atmosphere and give it a big boost towards orbital velocity.) The ability to place bulk cargo into orbit would give the US a tremendous economic advantage. (Selling solar power satellites, colonization of Mars...)

Ten miles from a flat surface? That seems a bit ambitious to me.