It was balanced triodes? The Gear Page where I heard about needing balanced tubes in the PI. ...
"Balanced Triodes" is highly overrated. Tube vendors charge more money for "balanced triodes" because not every tube they get will have balanced triodes. Buyers see a higher price and assume "costs more = more better."
I mostly spend time at The Gear Page now. The voices there range from "Very Well Informed" (including designers & manufacturers of excellent amps & other gear) to... ahem... "
Less-Well Informed." The reader can't assume all voices are equally credible.
At the bottom is a set of triode curves and some plotted loadlines. The tube stage investigated had a supply of 360v. Knowing nothing else beyond "it's probably good to idle somewhere in the middle of the loadline," we could guess 360v/2 = 180v as our plate voltage at idle.
When we know a bit more, we find that grid-to-cathode voltage of 0v is the guaranteed "onset of heavy distortion" absent a special circuit driving the tube-stage being investigated. The Red loadline in the image seems to cross the 0v grid curve (where "grid-to-cathode voltage" equals 0v) at about 60v on the plate.
360v supply minus 60v (at the 0v curve) = 300v. 300v / 2 = 150v (above the minimum plate voltage of 60v). 150v + 60v = 210v.
But the grid curves get bunched up in the area near high plate voltage & low plate current. That would mean distortion, and some will tend to stay away from that region. Talking about where the Red line goes above ~300v.
Okay, so now we have a working range bounded by 60v on the plate at one end, and ~300v on the other. That's 300v - 60v = 240v, and half of that (to bias in the middle) is 120v above the bottom of the range ===> 60v + 120v = 180v
We started with throwing a dart at "one-half the supply voltage" (180v), refined that by noting a lower-bound (210v), and refined further by noting an upper bound (180v) to arrive at the same place we started (mostly by coincidence than any "rule").
Generally, after accounting for any bounds on "acceptable operating area" when you want the largest possible output swing, and the stage in question is Class A, you shoot for something near half the available voltage-swing, or half the available current-swing.
These are some foundational concepts, but they're easy to breeze past when going down the rabbit hole with every element of an amp circuit.