From what I can tell, though Jerry left the wah cocked, he also moved the pedal over a very small range, not the whacka-whacka thing that I find so cliche. So, yes, there might be less an issue with leaving it cocked (though even then there are tonal differences), but I haven't found one that had that growl, that sweet spot with the emphasis I want in the smaller range of motion that I need.
I have owned two Budda wahs over the years. From my experience and from reading more than a couple of reviews, they all sound different. I have been doing some listening to sound samples on YouTube and such and seems, for the small amount I will use it and the cost, the Crybaby Classic with the fasel inductor is a very fine sounding pedal and quite inexpensive. Since I can find them used for cheap,I think I'll try that.