That’s another important variable for sure. I imagine that advocates for “use the smallest amount of pick possible” might be choosing not to use very much edge picking. Or they may not be aware of how little they are using. All other things being equal, the more edge picking you use, the more “depth of pick onto the string” or “amount of pick” you can use and still get a smooth consistent motion.
But the sonic desirability of edge picking can be subjective. Paul Gilbert famously LOVES the scraping sound he gets when he uses Tortex picks at .6mm or .73mm with lots of edge picking. There are other scenarios where for creative/sonic reasons, you might want to use less edge picking. I think it’s useful to explore how you can achieve smooth and consistent picking even with very little edge picking (even virtually none).
I think that in a scenario where you have very little edge picking, a very rigid pick, and a very stiff grip, it is still possible to achieve smooth and consistent picking. But I think in such a scenario, the smoothness of your picking become more sensitive to the effects of: consistency of “amount of pick”, resilience of picking motion to variation in string resistance, and maximum magnitude of “amount of pick”. Among these, I think consistency of “amount of pick” is probably the most important. The more consistent you can keep that, the greater the magnitude of “amount of pick” you can feel smooth with using your picking motion of choice (all other variable remaining the same).
I do think picking motions that use larger muscles and/or incorporate more arm momentum and/or a stiffer arm setup and/or a fulcrum further from the strings (i.e. the arm setup creates a longer lever to act against the string) for the pick stroke will be more resilient to disruption of any of the other variables. But the fact that there are so many famous pickers who achieve amazing results using movements that are primarily wrist (maybe with some larger muscles creeping in at the highest speeds), e.g. Andy Wood, Anton Oparin, Paul Gilbert, many others, shows that you don’t necessarily have to use a motion mechanic that looks like Joscho Stephan or Rusty Cooley to achieve smoothness (I’m not saying they use the same movement as each other, but both are examples of “bigger arm” type movements).
In thinking about “resistance of the string”, consider also what position along the length of the string you are picking. A string will be harder to displace (greater feeling of “resistance”) closer to the bridge, and easier to displace (less feeling of resistance) as you approach the midpoint of the string (12th fret). Other considerations come into play when making that choice as well (e.g. role of palm muting, whether you want to rest on the bridge or not), but it’s a variable to be aware of.
And for anyone wandering in from the street, it’s worth observing that great players typically feel their way into a solution that works for them using a trial and error approach that is less deliberate than what I described above. But maybe being aware of those factors can give some ideas for a few different things to consciously experiment with, and potentially feel your way sooner rather than later into “what works for you”.