I'm not sure exactly what Ron W's motivations were in developing the original Q circuit was, but you're all aware that in addition to his work at Ampex, he operated a recording studio as well, so he had access and experience with high-powered studio gear.
I wouldn't be surprised if the motivation were to develop a very characteristic alternative to the very simple conventional controls that were common at the time.
The Series filter is a low-pass filter that does something a passive filter can't do - it adds a very strong resonance around the corner frequency. That's what that pointy peak on the frequency response curve is in the old diagrams above. The basic flavor of the circuit is a regular low-pass filter. When you turn down a conventional low-pass tone control, you're sweeping the frequency of the filter downward and filtering out the highs. There's no bump at the corner freq, so the highs just sort of disappear. This is how the Series circuit works when the Q switch is turned to the 1st (or most off position) or a CVQ is all the way down.
When you flip the Q switch to one of the other positions, the EQ opamp is creating a pretty huge and narrow boost right at the corner frequency. If you turn the Q to the 3rd position and rotate the filter knob, you're shifting the corner frequency as before, but the resonant peak is shifting around with it and you'll perceive that as a wah effect if there's any output in it's range.
The circuit is not working like a parametric EQ, but, if you've used one before, tuning a parametric is often like what you hear using the Q-circuit - you boost or cut in a narrow, specific range, then slide it around to find where you want it to act, then drop the level and bandwidth to refine your tone.
So, with the addition of the Q-switch, you keep everything you had before (switch in pos #1) and get something new and totally different, but relatively easy to use.
There probably was some temptation to put a full pararmetric EQ on board, but it's more knobs, and more complexity in explaining how the controls interact to somebody who's not a gearhead. Same with having a bandpass rather than low-pass filter - useful for some, but a confusing knob that makes your bass freqs disappear for many. The sophisticated user can add a parametric or bank of parametric EQs in their signal chain, but everybody benefits by a simple to use knob that does something really unusual but doesn't screw up your tone too much no matter what you do.
Just a guess,
David Fung