This is a great discussion. My brief personal experience with two different grinders has been, like John's, that I get more consistent results day to day if I keep some beans in the hopper.
I started out with a Macap M4 stepless doser. I was simultaneously trying to learn how to make espresso and trying to evaluate lots of different coffees to see what I liked. I quickly dispensed with the hopper and moved to grinding by the shot. I used a Bumper rubber tamper stand with the tamper in it as a lid for the grinder throat. Without the rubber holder, the tamper would have contacted the nut on top of the motor shaft, scratching the tamper's stainless surface. Basically, with the M4, there's no way to weight a single shot of beans all the way through the grind without some sort of cylindrical device.
I had consistent problems with the grind setting needing constant adjustment with the M4, always from one day to the next and frequently during the same day or even the same session. This was true even after grinding about 10 lbs of coffee over a period of about 7 weeks. It seemed to take an inordinate number of attempts to dial in the grind, and it would change significantly from day to day, and not in a predictable manner. I had some issues with channeling, too, and had to resort to WDT (even with the GS/3, which is pretty forgiving.)
All this led to my trading the M4 for a Baratza Vario (on Jim's recommendation, I might add.) This is probably a temporary move while I wait for the next generation of more user-friendly conical, doserless grinders. The Vario is much more stable than the M4 and I feel the grind quality is significantly better -- fluffy, no WDT needed, etc. I started out using the Vario in single-shot mode, but found that the grind had to be adjusted every day, and sometimes between shots, even after a few weeks of break-in. Much more consistent than the M4, but still annoying.
So, I decided to abandon single-shot grinding and try putting 6-8 oz of beans in the hopper. The results have been dramatic: the grind setting is much more stable from day to day, and almost never needs to be changed during the same day. Sure, the grind has to be adjusted as the beans age, and sometimes as the hopper gets close to being empty, but it's much less frequent than before. Some days I have to adjust after the first shot, other days I don't. I feel like this is slow-motion compared to what was happening before.
Another advantage to filling the hopper is that I can use the timer. Turns out that once the coffee is dialed in, the timer is quite accurate and repeatable from day to day, well within 0.5g (closer to 0-0.2g.) I'm still weighing the grounds because I'm OCD

, but may dispense with that eventually.
The bottom line here is that I had to change my preferred preparation method to get the results I wanted. It's not the end of the world: being able to change coffee every 6-8 oz is fine -- it's at most 5-7 days worth of beans. If and when I upgrade to a top-of-the-line grinder, I'll keep the Vario for an alternate coffee or always-available decaf. My sense is that for non-cuppers, multiple grinders may be a better solution than single-shot grinding when you want to vary the coffee. I know I'm not the first to come to this conclusion.
Like John's observations, mine are anecdotal and unscientific, and unlike John's they're based on a lot less experience. The caveat is that the observations have been made while learning from scratch how to make espresso, and also while switching grinders and machines (and having some flow rate problems with the latter.) That's a lot of variables and moving parts.