I agree with all of that. Just bear in mind that the datasheet offers little or no information on how an opamp saturates and recovers from saturation. When Pro Co selected the LM308, it was either by listening tests or that's just what was available at the time. A lot of these fuzz circuits just happened. Pedal builders didn't use germanium because it sounded better than silicon. They used gemanium because that's all there was. Same goes for opamps. JFET opamps were rare and expensive when the Rat was developed.
Dunno if this story is less truth and more story but
“A quote from the Book 'Stompbox' by Art Thompson, published by Millar freeman Books. The passage starts 'Scott Burnham's story';
"I had the basic circuit roughed together and I'd found an op-amp I liked, the LM308N, which was an instrumentation amp used for seismic and medical sensors. I was experimenting with an EQ boost for this op-amp in order to pre-boost the treble so I could use just a passive tone control to cut back the highs. i was bypassing the voltage divider that sets the gain when I picked up a resistor, looked at it and thought to myself, "yellow, violet, brown - thats 470ohm." I plugged it in expecting to get about 50dB of gain, but when I picked up my strat and hit a string , it went wooooo. I thought, " Holy shit, this is cool. What did I do?"
I looked real closely and realised that I'd plugged a 47ohm resistor instead of a 470ohm resistor (sound familiar
). That meant it had somewhere around 70db of gain , which, according to it's spec sheet was impossible from that op-amp. Trying to set the gain on this thing I had stumbled across a combination of resistors that produced this really weird high-frequency shelving boost that the op-amp couldn't possibly sustain. It didn't have enough slew rate to produce that much gain at those frequencies so it drove the op-amp into incredible slewing distortion. This usually is very bad , but in this case it gave the Rat it's yeowl - I've never heard any other stompbox make that sound."”
via
https://www.diystompboxes.com/smfforum/index.php?topic=55234.0
but yeah happy accidents like that are the exception and not the rule (and I’m sure selecting the LM308 in the first place had as much to do with cost as it did with sound). “Mojo” parts aren’t rare because they’re “better”, they’re rare because newer better stuff replaced them.