Because KABOOM.

Intimately mixed fuels and oxidizers are pretty much indistinguishable from explosives, and in particular, LOX mixed with flammable hydrocarbons is an incredibly touchy explosive that can be set off by shock, vibration, or having a light shined at it. There is no chance you could get it through the turbopump. Let alone load up a rocket with it.

(This issue destroyed the Bell X-1 rocket plane using a much less flammable hydrocarbon that wasn't thoroughly mixed like that.)

Additionally, RP-1 is going to freeze at LOX temperature.