He wasn’t losing the war any faster than Mussolini, who went into WW II with tanks that needed sandbags and a lot of inferior equipment [and generals and admirals]. And since Germany was the principal British opponent [by ‘43 Mussolini was a sock puppet], going after Benny instead of Adolf makes no sense, assuming an assassination attempt was going to made.
Perhaps they took the view that Italy’s alliance with Nazi Germany was very much Mussloni’s personal policy.
Italy’s alliance with Nazi Germany collapsed very quickly after Mussolini’s downfall. Even if Mussolini was an incompetent boob at running Italy’s war effort, the fact that he was keeping Italy in a war the Italians didn’t want to be fighting made him dangerous enough to be consider taking him out...