The combination of Methane and the full flow staged combustion cycle also means significantly reduced coking in the engine, so it drastically prolongs the time between engine refurbishments.
Do you know how a reduced coking works? I've read about the raptor engine[1] and it explains how fuel rich hot mixture leads to coking, it explains how USA solved this problem before (by using hydrogen as a fuel), but how Musk managed to solve it? Partially burned methane should produce free carbon atoms, shouldn't it? Doesn't it raise a coking problem?
In a conventional hydrocarbon fueled engine, you're using a fuel with hydrocarbon chains at approximately room temperature to cool the engine. With only a little heat addition, you get up to a temperature where these chains can shed hydrogens and convert their C-C-H bonds to C=C double bonds. These bonds in turn allow hydrocarbon chains to join together into larger molecules that can coagulate and stick to the walls.
Methane on the other hand is starting out at a much lower temperature, and it's very difficult to get methane molecules to react with each other to form large molecules as you're not starting with any single C-C bonds. Isolated free carbon atoms (soot) aren't much of a problem.
According to the link above they do. Full-flow means to have two pre-burners one going fuel rich while other going oxygen rich. Though I'm not a rocket scientist and I'd be grateful if proven wrong.
[1] https://everydayastronaut.com/raptor-engine/