Added to that, Full-flow stage combustion engines are bigger, heavier, and more expensive, but are way more efficient. So a bigger rocket is the only option to get one of those onboard, and helps with taking more mass to orbit because they are more efficient than other options.
I don't believe there's any performance advantage for full-flow, which SpaceX alone is attempting. The only point is to lower the combustion temperature inside the turbines, at the expense of (much) higher flow rates through those turbines, in order to increase their lifespan.
(There's a large difference between staged combustion generally and gas-generator engines, which throw away performance by dumping fuel out of the turbine exhaust).
Since the temperature limit of available materials is the fundamental limitation (even after making custom high-temp alloys), this allows them to maximize mechanical power from the turbopumps, which raises performance.
We might imagine a conservative FFSC design which accepts very low temperatures in exchange for making it easy (low R&D cost) to reach high longevity. Raptor is not a conservative design, so it requires more R&D to achieve that longevity.
