So, then, I gather that the so-called turbo brush attachments are not so effective unless they are electrically powered.

Automobile carpeting is quite rugged, I have used a steel brush effectively in conjunction with the powerful shop vacuum.
On the carpeted steps, as the steps are economy sized(for poor people), vaccuming is not easy.
And the middle weight Optima 430 struggles with this task.
Their accessory "turbo brush"($22 or so) may help on the small steps, but, from what I read, I think not......

Mr. Dyson had the same problems with the turbo brushes available, so he invented his own. The Dyson-built Mini Turbine Head works flawlessly, year after year. Mostly because the dirt does NOT pass through the turbine blades (unlike any other turbo head). I have an adapter to use the Dyson head with other 1 1/4 inch wand cleaners, and have used it with great success on most of my cleaners in the collection. The Dyson-built turbine head for the car (included in the car cleaning kit from Dyson) actually spins the brushes FASTER, the harder you press down. Again, the dirty air is NOT drawn through the turbine, so picking up rocks and coins does not bother the Dyson Mini Turbine Head(s).