I'm not a great fan of longhand calculations posted here in this style. it's a very lazy way of thinking out load. You really ought to have a distinct point that you're trying to make, and to make it simply.

That said, if we look at what you've done - you've ignored the whole point of the rocket. It doesn't just LIFT the mass, but it also accelerates it. If the engines cut at the point where the rocket had reached 1 km, it would keep going balistically for several more km. So the fuel efficiency is much better than you calculate.

What you've done is the equivalent of saying that a top fuel dragster is inefficient because it burns more fuel to do the quarter-mile than does a family saloon car.

Of COURSE it does - that's the whole point of what it does - it goes fast.

So do Rockets.

Maybe if you go away and calculate things out properly, then come back again, we could have a useful discussion? There's fertile ground here for theoretical lifting mechanisms like a space elevator to be more energy-efficient than a ballistic rocket, and there are interesting reasons why things are done the way that they are...