The basics of your argument are true, but the air breathing capabilities change the magnitude of the effect quite a bit. Saving the oxygen weight in the 'first

The basics of your argument are true, but the air breathing capabilities change the magnitude of the effect quite a bit. Saving the oxygen weight in the 'first stage' helps a lot. One oxygen atom has a molar mass 15 times larger than one hydrogen atom. Burning O and H to H2O thus means you have 2/17 of the mass laying in the hydrogen, 15/17 in the oxygen. It's an order of magnitude savings. Again, look at the Virgin Galactic Spacecraft as an example. The reason why they can go so high without much of anything, is that their first stage is an air breather. Furthermore, the fuel that you need to bring to go from Mach 5 to Mach 25 is what's responsible for a large size increase of your first stage - to have more fuel to burn at a high altitude / high velocity requires even more fuel at the ground. Overall, you have to look at an airbreather quite differently than conventional rockets and you have to look at suborbital flights differently than orbital - you can't really approximate it from the space shuttle without going into the details.