I'm too old and my knees are too wonky for such things; "give me gears, lots of gears, and some hills to ride upon....."
Ahem...Anyway, "fixies" used to be a standard training item. It was the usual practice for road racers to spend the early part of the Spring training season on fixed-gear bikes, to build up leg speed and improve circulation before going to harder training.
At least, that was the case in some of the older books I read; I have no idea how pro road racers train now.