Right, I follow. So the first answer I suggested was the correct one...you need to inject at high pressure, else you can't overcome the high pressure of the combusting propellants in the chamber and can't get any more propellants in.

And I see what you are saying about the consequences for the tanks, etc. if you have a gas-pressure fed design.

I suppose my conceptual troubles come in part from the fact that rocket equations (like Tsiolkovsky) use the exhaust velocity, and this is usually given in basic texts as being dependent only on the propellants, i.e. determined by chemistry not engine design. Therefore, in my mind, if you burn X and Y you get a reaction whose products have an energy determined by the chemistry alone, and this relates to a certain value of kinetic energy and hence exhaust velocity; and this will happen at whatever pressure you burn X and Y.

I guess I have not been able to reconcile this small-scale molecular view with the bulk view of the engine. In this view, it is clear that a higher combustion chamber pressure will result in gases emerging with higher exhaust velocity, as is the case for a jet engine or gun, etc. (Although in a rocket engine, you have had to expend some energy achieving those high pressures).

So I have one model of an engine where it is clear that you want a high combustion pressure (and you have explained why pumps are the way to get that for a large engine); and one model where it is the chemistry alone which matters in achieving a high Ve. What I lack is a way to fill in the gaps between those two views!