The AC frequency on an inverter power source can be varied considerably. For example a Dynasty 200 DX can be adjusted from 20 - 250 Hz. This allows considerable flexibility in tweaking the arc shape and performance when using the GTAW process.
A simple transformer power supply will simply output the same frequency as the input line typically 60 Hz (or 50 Hz in some countries). I would guess that AC welding rods were developed for use with 60 Hz long before inverter machines were available. So the question is...
Would there be any advantage to running a SMAW rod at a higher frequency? Or perhaps with high frequency stabilization? Or advanced square wave vs. a sine wave?