For the amplitude there are a few methods to choose. Sync rectifier, precision full / half wave rectifier, peak detection and maybe a thermal converter. With low distorion one is free to choose a method different from RMS and still get a stable amplitude. Just for stability the distortion would not even be that critical for stability.
And since AC voltmeters are using the same methods, it isn't like something better or unavailable is needed.
On the subject of precision rectifiers, the open loop gain element can be AC coupled at the input *and* output to remove offset voltage.
I own two Krohn-Hite audio generators that directly generate in-phase and quadrature outputs. The AGC feedback uses a sample-hold on one output triggered by the zero-crossing of the other to get a DC output with low ripple.
I have thought about doing the same thing for calibrating the output of a pulse generator in place of precision resistor networks.