> "But why do we consistently see certain OT primary impedance with certain tubes?"
An audio power pentode with G2 near Plate voltage has a "minimum" load it will pull happy. Typically, per side, several times HBP's "grid line represents ~270 Ohms below the knee". If "several" is 4 or 5, a 270 Ohm below-knee line can pull a 1,250 Ohm per-side load, which is 5,000 Ohms plate-to-plate.
Higher loads work, but less Power, unless you raise the supply voltage. There's limits how far you can go. First, certain voltages are commercially "easy", mostly descending from 450V limit on electrolytic caps. Second, if you raise the G2 voltage along with the plate voltage, available current goes up, but with the higher load impedance the required current goes down, meaning you potentially have much more current than you need. At a minimum you will need larger G1 voltage to control normal operation. When things go wrong, a high G2 voltage makes them blow more smoke more faster. (There's also a max plate voltage on the tube, but that's not usually the real problem.)
> The tube charts specify a plate-to-plate impedance for a reason.
That is a condition the junior engineer documented on the test-bench. Since he wanted to stay employed, it is the "BEST!" that he could make that tube do for a given supply voltage or other design-goal, without dangerous swings (which would burn tubes and that would be bad for the tube maker) or absurd conditions (5K, 6.6K, but rarely 5.6K until 6L6GC data sheet).
You really "match" the OT load to the power supply. If some low-V high-I PTs fall off a truck, you look for a low-Z OT to go with them, and vice versa. Extremes may also have you looking for extreme tubes (6V6 will never drive a low-Z load well).
As for tubes, with pentodes you won't be far wrong if you find the Triode plate impedance for a high current high power condition, then pick an OT about 4X higher p-p, then aim low. HBP says 6L6 triode runs around 1.7K. 4X is 6.8K. Indeed 6.6K is a popular load. 5K also works well. Fender ran 4Kp-p by working G2 at very high voltage (which needed 5881 or 6L6GC types, not the original 6L6 recipe).