> I'm surprised that nobody seems to have used preburners to pressurize the tanks
This combines the worst of both worlds. You get the weight and complexity of turbopumps. And you get the weight, explosion risk and leakiness of pressure vessels.
This combines the worst of both worlds. You get the weight and complexity of turbopumps. And you get the weight, explosion risk and leakiness of pressure vessels.
Pressurizing has weight advantages. You can use a balloon tank. The tank no longer has to have the rigidity to support itself.
Rockets with typical cycles have used balloon tanks. Even modern ones like the Falcon 9 are partially that way, with just enough rigidity to be erected empty on the pad. The Falcon 9 uses helium to pressurize; that could be changed to preburner exhaust even if you did keep the moderate pressure and the turbopumps.
Pumps are still good because you really don't want the tanks to pressurize at the same pressure as the combustion chamber. If you do, you'll see a rapid disassembly, but your claim on it being unscheduled will be questioned.
To drive the flow of fuel and oxidizer into the combustion chamber, you must overcome the pressure inside. To drive this flow, the turbopump output pressure will be of comparable magnitude to the combustion chamber. This pressure is in the realm of a few 10s of megapascals, or a few thousand PSI. This is a hard design requirement.
If you're proposing to "skip the turbopump", then necessarily you'd have to pressurize the entire fuel and oxidizer tanks to these high pressures. This is, to put it very mildly, utterly infeasible.