The closer you can keep point of contact to center of the flat, the better for torque transfer, which will help to not break fasteners.
You got that backwards. When the socket contacts the bolt closer to the corners, you get less stress (trying to split the socket or rounding the bolt head) for a given torque input. Snap On Flank drive sockets hit pretty close to the corners.
Other sockets fit looser and contact further in from the corners (nearer the centerline). This results in much higher stress. Just a tiny fraction of an inch can greatly increase the stress since the force is equal to the input torque/distance from fastener centerline to the point of contact. I think Snap On has said 20% less stress in the past. It could be something like that (compared to craftsman for example). A few thousandths of an inch could make an appreciable difference.
By moving the contact point away from the thinnest point in the socket wall, and eliminating a sharp angle, you increase socket strength and reduce breakage.
Not quite right either. If the load at the contact patch was the same, this would be true. But it's not. The closer you get to the actual corner of the bolt head, the lower the stress, the lighter and thinner you can make the socket.
As far as rounding off corners, how loose would a socket (especially 6-point) have to be to round off a nut? Flat sides would have to pass over/tear off the corners. That's a lot of metal to move.
Not that loose. All sockets contact hex heads with a very thin line on each face of the hex. When you apply a load to a surface, the resulting stress equals load/area. We can assume, due to the manufacturing tolerances of a bolt head, that most sockets will only touch 2 flats (initially). So the area of contact is TINY- like the breadth of a human hair. As contact area decreases, stress increases. So it's not hard to generate enough stress to plastically deform soft metal. So a std grade fastener is fairly easy to round over. The other issue is the orientation of the socket flat - the angle between that and the bolt hex. As that angle increases (due to a sloppy fit or pre-rounded corners), the chance of rounding the head increases dramatically.
When a fastener rusts, it looses metal. The rust initially increases the dimension, then rubs or flakes off leaving less hard material. This allows a socket to rotate more and present the corner of the hex head bolt with an angled surface (for normal pre-FD sockets). The corner has less material behind it, so less strength. As it yields the contact patch becomes closer to the center of the fastener, so stress increases, more yielding etc.
The flank drive socket actually works like a Flank Drive Plus wrench. The contact point inside the socket is a sharp edge that actually bites into the socket (instead of the angled surface above) like a tooth. This creates a lot of friction which helps the socket grab on.
Here's one more thing to think about:
When you apply torque to a bolt via a wrench, in Freshman physics we learned that that same torque must be reacted by the bolt (in friction for example). But in the real world, that isn't true.
Every part in that system bends and flexes elastically. The ratchet bends, the pawls inside its head compress slightly, and the bolt head is squeezed. If the socket contacts the fastener just a tiny bit closer to the fastener centerline, you get more stress so more elastic deformation of the bolt head. This means you actually need more effort to remove a bolt with a lower quality socket.
We hear stories from old pros all the time about how their Snap On socket removed a fastener others' could not. Or that they can remove stubborn bolts with less torque. This is why.
Just to put this in perspective, I'm not sure how much additional torque is required to crack a stuck bolt free using a craftsman socket versus a Snap On. It could be fairly small which also explains why guys can get by using regular grade tools. But to respond directly to the OP, why would one choose an inferior socket to a modern FD style version? FD sockets do a better job of removing stuck fasteners and do it with less effort.