I still do not understand why this added voltage cannot be controlled with series resistance at any point in the output circuit.
It can if you are careful. Try this -
Most people are familiar with a home stereo power amplifier. This is an almost pure voltage source, and has a very low output impedance, almost equal to a theoretically perfect 0 ohms. It is so far removed from the vacuum tube amplifiers that were the standard when the physics of impedance matching were worked out that those concepts do not apply. The voltage across all speakers, 4, 8, 16, 32, 60 ohms, whatever, is the same. Thus, as the speaker impedance goes up, the maximum power delivered *at the speaker* goes down.
PA systems are the last remnants of the empty-state device era. A tube amplifier is an imperfect current source, not a nearly perfect voltage source. To get the maximum signal power out of a tube amp, the Maximum Power Transfer Theorem (MPTT) applies. The tube output stage has a relatively high output impedance, and a speaker has an inherently low impedance. To match these two efficiently for max power transfer, the impedance of the load must match the impedance of the source. Thus the 4-, 8-, and 16-ohm taps on the secondary of the output transformer.
A PA system has other constraints, chief among them the fact that they often are "designed" by people with no formal EE training. This is wny the speaker transformers are rated in watts. The idea is that if you have two rooms of different sizes, and experience or calculation indicates that for approximately the same perceived audio volume in the two rooms one needs 5 W at full volume and the other needs 10 W, then use transformers with those two ratings with *any* PA amp 70 V output, and the volumes will balance. All PA amps make the same 70 Vrms at full volume. The only difference among them is the amount of available current, but having transformers with inputs rated in watts and output taps for various speaker impedances eliminates all of the usual load-matching math.
Yes, you can connect an 8 ohm speaker without a transformer - IF - the series resistor is such that the minimum resistance seen the amp output is greater than 83 ohms. For example, an 8 ohm speaker with a 75 ohm resistor will not damage the amp. However, for every watt of audio power in the speaker, the resistor will be dissipating approx. 9 W. When the amp is making 60 W, and almost certainly overheating, the speaker will receive only 5.8 W.
ak