This certainly wasn't true for cars, a fully electric vehicle is simpler, resulting in an immediately noticeable reduction in maintenance overhead - are you sure it will be different for aeroplanes?
Keep in mind that the combustion engine of a propeller aeroplane will have an entire electrical system as part of the combustion engine because it turns out even most private pilots are not inclined to get out and start the propeller by hand ever time.
I work in the UAV industry and would adopt variable pitch in an instant if it didn't come with complexity and weight penalties!
Now an electric motor has maximum torque at 0rpm (stalled) and practically no torque at it's no load speed. The relationship in-between is practically linear. So long as the motor was matched and / or geared so that during all stages of flight the RPM stayed within a reasonable band I don't see what the advantage is. Maybe some second order effects of efficiency at lower speeds perhaps.
Edit: Actually, thinking again, it's the exact same reason that cruising at the lowest possible RPM for the required power output in a piston engine is typically the most efficient. Just less friction. Still think it'd be a smaller effect given we're talking roller bearings rather than plain bearings and piston rings.
Unfortunately I'm traveling at the moment, but I spend a large amount of my time at work balancing propellers and motors and could provide some plots that might help explain this. One of the few things years of working in academia proved to me, is that I'm terrible at explaining things like this!
EDIT: Yes, I was surprised as well. IIRC the service plan for a new car was more than a thousand euros per year. Considering they don't do oil changes or many other things, that is a lot.
Anyway, maybe not much for someone who spends 70 000 euros on a new car, but it's something that does not further the argument of economics.