Some very astute observations.
In the case of EdgePal (the first original commercial design of such an implement) , you have an attachment for a file. I think it is optional, though.
Depending on how much of the stone you drag across the edge, you will have more or less degrees in the "sphere" you are sharpening. You can get a convex where the tangent to your "starting point" is x degrees, and at the very edge you have for example 3 degrees more.
Adjusting the angle, you can treat each segment of the edge to your liking. More "meat" where you want, and less where that's to your liking.
However, I can see why a skilled eye and hand would forego this precission and do what is already instinctual

. But the geek in me likes all these gadgets that result in higher (and unecessary) precission, on an axe. Though at least they help me get a decent edge on a knife, free-hand sharpening being something beyond my abilities, not that I've investd a lot of effort towards that. An axe...for some reason it seems simpler to sharpen. I just use smaller stones in circular motion.