In SSME, most of the LOX never goes through a preburner.

The SSME uses the same kind of fuel-rich combustion chambers for both preburners. This presents a problem for the oxidizer side because any leaking along the shaft between ox pump and turbine in either direction would be catastrophic. This is resolved by an extremely expensive and complex multi-stage helium-purged rotating seal.

One of the cool parts about most FFSC designs, and the raptor in particular, is that they can afford slight leaking from high pressure to low pressure through any seal in the system and it's broadly safe, and only marginally reduces performance. This allows them to be made much more cheaply.