[Mondial]

A lot depends on what type of mixer/osc the radio uses for the converter. A pentagrid tube like a 6A7, 6A8 or 6L7 is very noisy internally and a radio using them benefits greatly from an RF stage since it increases the signal level into the mixer, overcoming the noise.

The Philco dual triode converters of the 40's are much quieter and there is little to be gained sensititivity wise with the addition of an RF stage. In this case the second IF is really useful as it adds gain and selectivity while preserving the low noise and high overload characteristics of the triode front end.

Oo the other hand, the tuned RF stage increases image rejection and is very helpful in this regard, especially in the short wave bands where images are always a problem in single conversion receivers.