Fluoride is impossible to run oxidizer rich, to drive the turbopump. The Raptor is gas gas. So you need to preburn both fuel and oxidizer. Abd here is where CH4/LOX combo shines. Turbine power is, for a given input and outlet temperature, mass flow * specific heat. RP-1 can't be run fuel rich at staged combustion pressure and heat. H2 is great, but it had 14 vs 0.9 for LOX. Since O/F is 6.0, you have too much power on the H2, and too little in the LOX side. But CH4 has about 2.1 with an O/F ratio of 3.2. So your power is very balanced and you can push the system a 50% more.
Either 50% more chamber pressure for crazy performance or 35% lower temperature for longer life, higher reusability.
Lastly, if you take 1kg of H2 to mass, you'd be able to make more than twice the propellant if you mix with CO2 to make CH4 through the Sabatier process, than if you simply extracted the O2 to make the LOX. Not to mention that CH4 is way easier to store than H2 while you produce your propellant and wait for the craft to arrive.