Brief History of Tremolo
Someone thought it would be cool to change volume cyclicly, like a singer's tremolo.
Short-path to changing volume of a tube is to turn it more-on, then more-off. This can be done by changing the bias of a tube. Preamp tubes have the smallest bias voltages, so they also only require the smallest trem signal to get the job done. So first-pass might have been injecting trem at a preamp tube cathode, as in the Fender VibroChamp (and many earlier amps from other companies).
You could inject the trem at an output tube cathode or grid, but the signal needs to be very much larger. Or, as some companies did, you could inject trem at some other point which changes a tube's gain, like the screen of a pentode.
There's a problem with injecting trem like this into a single-ended (or unbalanced) circuit: the amp has a "pumping" or pulsating background noise. You could cancel that background noise if it was applied to a stage which only responded to push-pull (or balanced) signals. Leo Fender actually patented the 5E9 Tremolux tremolo... The 2 sections of a paraphase inverter don't have to share a cathode resistor. But if they do share a cathode resistor, trem can be applied there to varying the gain/volume of both sections at the same time (and also save the cost of a resistor). If the paraphase is truly balanced properly, the trem pumping is common-mode, but the output section of the amplifier only responds to push-pull signals, so the pumping noise is cancelled. So that's why it's injected at the shared cathode of the paraphase stages.
The change to the long-tail pair inverter probably accompanied bigger output stages with higher B+ voltages, corresponding larger bias voltages and bigger output power. You could inject trem across the "long tail" of this inverter, but injecting it only across the self-bias resistor in a long-tail requires a trem circuit with a floating ground (big hassle), while injecting across everything from inverter cathode-to-ground take a HUGE trem signal. And where the trem signal reduces the tail voltage, it throw off the balance of that inverter. So we're working really hard to throw noise back into our amp; instead, the trem injection gets moved to the shared point of the push-pull drive to the output tubes. Namely, the bias feeding each output tube. Now we're back to common-mode trem variation, with background noise largely rejected by a push-pull stage leaving just our signal plus trem. You'll see this circuit in the 5G9 Tremolux, as well as a number of the smaller Fender amps with volume tremolo.
This is still a lot of work and extra tube stages to drive a low impedance part of the amp circuit. And with very big output stages, it might not be enough to get strong trem. And so along comes the opto-isolator trem to ground/un-ground the signal before it gets to the phase inverter. You'll see this in most the mid-60's in amps in the Deluxe and higher power ranges. In theory, the optoisolator doesn't add to the noise, since it's subtractive in nature (though you'll often hear background hiss from other sources in the amp rising & falling).