I don't get it. Your body is only maximally efficient at one cadence. So a single speed or fixie is only efficient at one speed.
How does a fixie help your pedalling? You're connected directly to the rear wheel which uses the momentum of the bike to force your feet around the crank spindle, rather than the other way round.
You can blow out your knees mashing up a hill or into the wind on a single speed.
Using a fixie for training is like using a single shot rifle on the range and then switching to an AR-15 when it's for real.
Fixieism is an urban fad. Like all fads, it'll die a well-deserved death.
Make mine ten speed Ultegra.