Yes, ullage is king here. All the pumps in the world won't help you if the fluid you're trying to pump isn't anywhere near the pump inlet. Not only do you have to consider pump head pressure, which you can solve with staged pumps, you have to consider that propellant slosh may deny you any use of pumps. This is especially true if you have to plumb the tank for both horizontal and vertical operation. The abstract principle of the header tank is very simple: the fuller the tank, the less likely propellant slosh is a factor, and the less likely tank outlet location is a factor. If the tank is sufficiently small, you can even introduce technologies like bladders, which effectively eliminate all the slosh, but I don't know if SpaceX are doing that.
So burning the Raptors longer on landing obviously means more propellant in header tanks that can't be touched until landing. But since it all has to fit in the same fuselage, it means less fuel available for ascent -- the moneymaker. Also, the flight dynamics would be altered by more mass in the header tanks. And at a certain point, moving them around the fuselage for weight, balance, and moment-of-inertia purposes will typically either get you in structural trouble or plumbing trouble, or both.
And you aeronautical guys need to quit being so modest. Fuel and oil flow paths and pumping strategies for high-performance aircraft are exactly the problems being solved here. Rocketry used to be easy. You were either ascending gracefully at 3+ g along the rocket axis, or floating in microgravity with no presumptions of favorable propellant placements. Starship's propellant feed system reintroduces the problems of aircraft fuel-feed systems. Hybrid thinking is needed.