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.

> Partially burned methane

The raptors don’t run fuel rich, which should reduce that 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.

Oh that’s interesting, do you have some more information or a link?