I think you're underestimating the pressures involved here by several orders of magnitude. To drive the flow of fuel and oxidizer into the combustion chamber,

I think you're underestimating the pressures involved here by several orders of magnitude. 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.