[sudosysgen]

If you wanted to efficiently make an efficient deeply variable speed modern motor run on AC, you might very well turn the AC into DC then back into AC in a brushless motor controller.

Indeed, changing the frequency of an AC wave programmatically is incredibly difficult (but possible through a CVT, I guess), you're better off turning it into DC then back into AC through some some form of function generator.

So indeed, the widespread use of BLDC motors is a point in favour of DC electric circuits in the home.

Same goes for variable velocity generators, you will generally have an AC-DC-AC conversion in a variable speed generator. Either that, or a gearbox, those are your two options.