I use one too.
Without it, especially with really light road rims, it’s possible to build perfectly straight wheels with hugely out of wack tensions. Alternating between truing and tensioning gets a true wheel with as near as possible even tension. Even if the spokes were perfect you’d still get a variance from some parts of the rim being stiffer than others. And all you need is a reading in the correct range as you’re going to go back and add/remove tension to true it anyway, you wouldn’t adjust tension as your final step.
I don’t really understand his argument though, obviously thinner/thicker spokes will affect the tension readings, but they’ll also affect his guesswork when squeezing them, or the tone produced by plucking the spoke, they’re all fundamentally measuring the same thing which is how easy that particular spoke deflects. It’s not the tension meter, it’s the spokes.