[votingprawn]

There would still be benefits to variable pitch propellers with an electric motor (motor efficiency, correct propeller pitch for the airspeed to name two).

I work in the UAV industry and would adopt variable pitch in an instant if it didn't come with complexity and weight penalties!

[VBprogrammer]

Interesting. I've always thought of variable pitch propellers as being more efficient by allowing the engine to stay at it's peak horse power. For a piston engine this is obviously at the peak of the nice curve you'll see on any dyno run. A fixed pitch propeller sized for climb would allow the engine to run above this speed in cruise and vise-versa if it were pitched for cruise.

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.

[votingprawn]

Even if you disregard motor efficiency (which I don't, as with a battery powered vehicle you treasure every Wh more than you treasure every gram of fuel!), propeller efficiency is also important. Ideally you want to match your motors power handling and efficiency with your propeller. A given propeller/motor combination will have a design point in terms of torque/airspeed/rpm, and operating significantly outside of that (e.g. having a power system designed for cruise but operating at zero airspeed) has penalties.

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!