That sounds fishy to say the least. The RD-191 for example can only throttle down to 27% not 10%.
I guess I did not make myself clear. The whole idea is to use a common LOX/Methane first stage engine across all the rockets instead of the combined LOX/Kerosene and LOX/Hydrogen engines currently used or contemplated. The LM-7/8 use the YF-100. The LM-5 uses the YF-100 and YF-77. The Long March 9 will use YF-130 engines. That is three engine types you need to manufacture and certify. This way you need a single engine type for the first stage of all those launchers. That is why I said "common first stage engine" not "common engine".
What SpaceX does with a common first and second stage is kind of beyond the point. SpaceX doesn't want to spend the engineering resources to develop a whole new rocket engine for the second stage which will be manufactured in small numbers and would require the use of different fuel. It is much harder to have ground handling facilities for hydrogen than methane. Just look at the boiling point of both. Methane has similar boiling temperature range to oxygen. Hydrogen is way, way lower. 20.28K for hydrogen. That is 20 degrees above absolute zero. Methane is 111.6K. Oxygen is 90.188K. The Chinese already have hydrogen production, ground handling, and the second stage engines already are in production. So the calculus isn't the same. LM-7 uses the same YF-75 engines on the LM-3A/B/C. The LM-5 uses the YF-75D, which is new, but it is capable of multiple restarts unlike their previous engine.
The move to a common first stage engine has nothing to do with saving fuel cost. It is all about driving down production costs through reducing the types of parts you manufacture. If you have those YF-130 engines only on a LM9 rocket which is launched like only once every couple of years how much do you think you will need to spend to maintain those production facilities, tools, and retain trained staff specialized in manufacturing those engines? The costs will be immense. It makes no sense. They need to rationalize the production chain in the future.
The 5m fairing production cost reductions because the diameter is same as LM-5 have nothing to do with sharing the tank design schematics. It has to do with sharing tools, production facilities, and logistics facilities to move things around. They have existing tooling dimensioned for that already.
If its about simplicity
The CZ-7 was meant to be a simple re-engine of the CZ-3 didn't turn out that way when they actually started looking at it and it turned into a whole new launcher.
If its about economics
All the engines you mention already exist and are proven so the R&D cost is sunk, production facilities exist and are paid for so that's sunk cost too, what would the ROI be to develop a common methane engine and integrate it into new launchers for mass production? Can it be achieved in the requisite time scales? i.e. does it fit with the goals of the space program?
Current systems provide the necessary capabilities for the projects in hand so looking into the next phase.
What kind of lift capability is needed to build a moon base does a new methane engine development cycle help that at all? or would scaling up the YF-77 provide what's needed? What's the relative risks and time to realisation of both approaches?
If the answers to any of those questions is in the negative then it won't really happen in the current development cycles because it provides no actual real world benefits.
Unfortunately, the real world often intrudes on sound ideas which is why we're nowhere near having world peace!
It would be different for commercial Chinese companies (the actual equivalents to SpaceX) which would come to things with a cleaner slate/more greenfield starting point.
That said Western media likes to hype Space-X and Blue Origin because successive administrations have royally screwed NASA over and having to pay the Russians to use Soyuz and use Russian engines in their heavy lift boosters doesn,t gel well with the 'we are the best' news fodder you can feed your populace. So when those fledgling Chinese commercial companies' prototypes start blowing up like starship there will be the usual 'Chinese made crap' narrative and spray painting of Space-X's failures.