The cost of fuel is negligible compared to the cost of the rocket.
Here are a few energy densities in MJ/kg
Kerosene 43.3
Methane 55.5
Hydrogen 142
So we can see Methane has 28% more energy than Kerosene.
And remember a rocket is carries a lot of fuel in terms of weight.
Any weight saving translates directly into increased payload.
What I talked about was the complexity of
operating and maintaining three liquefied gas (O2, H2 and Methane) in gelgoog's proposal (common
first stage) than two (O2, H2) in a CZ
in a launch facility. Your reply is unrelated.
hkbc has answered your post very well. Methane is not the best in first stage, nor the upper stage (2 and or 3). It is ONLY best for the specific scenario such as only one fuel to maintain rather than Kerosene+H2.
Also, fundamentally people in rocketry talk about specific impulse in vacuum and mass specific impulse at sea level, not energy density. In this regard, Methane is worse than Kerosene at sea level and worse than H2 in a vacuum. This is a well-known fact. It has been repeated by Chinese studies in their road-map planning, a reason why China tested a 70t methane engine long before SpaceX, but choose not to continue. China does not see the meaningful advantage of it even for a full flow engine like Raptor.
Now China conducting study on Methane engine is a continuation of the strategy of 技术储备 (prepare the capability for possible use one day). It should not be overstated that China has changed mind and acknowledged the minimal and conditional advantage that Methane engine has overcome its drawback.
Another reason (not related to your post) why China does not see Methane engine much wanted is the "re-usability" advantage of it is a myth propagated by SpaceX fans. Oxygen rich close circle Kerosene engine has no more problem than Methane engine. That's why you are seeing YF-100 being developed to 10% for re-usability.
All this is to say that, China want to be prepared some time in the future for the next generation rockets in some decades, but not today. And CZ-5/6/7/8/9 and 921 will serve a long time (two decades) before being replaced, and Methane is not necessarily the only one candidate.