Pe,

At first, I agreed with you. But, my guess is that the rear prop could end up working with only disturbed air from the forward prop. I made a quick sketch to show the reduced column of disturbed air from the pressures of the forward prop. My guess is that this column of air would be the swirling slipstream, or P factor air, also further disturbed by the fuselage. This could mean that the rear prop would experience uneven pressures around the disk. This could lead to vibrations and unequal efficiencies.

I've not seen this explained, so it is all a guess. It would seem that an equal sized or larger rear prop would bring in clean air near the blade tips to equalize the airflow more. I'm sure this has all been figured out much better.