Well, it makes the eggs go further for one...
But it also produces softer, creamier results. You're moving toward something like a custard or quiche. If you like your eggs very stiff, this is probably a bad idea.
Soften. Other things that typically are added with salt will tend to toughen the beans, but it isn't the fault of the salt. For decades, chefs have circulated the oral tradition that adding salt hardens beans, but it's a myth.
Several scientific studies verify that adding salt to the soaking water for dried beans will reduce the cooking times. The first and most cited article, originally published in 1977, can be found here. As mentioned in the first answer you cited, the fine folks at Cooks Illustrated found in 2008 that 3 TBSP per gallon of water produces soft skins while not over-salting the interior of the beans. Since you can't see the full article, here is the science according to CI:
"Why does soaking dried beans in salted water make them cook up with softer skins? It has to do with how the sodium ions in salt interact with the cells of the bean skins. As the beans soak, the sodium ions replace some of the calcium and magnesium ions in the skins. Because sodium ions are weaker than mineral ions, they allow more water to penetrate into the skins, leading to a softer texture. During soaking, the sodium ions will only filter partway into the beans, so their greatest effect is on the cells in the outermost part of the beans."
Harold McGee's NY Times blog (August 9, 2008) also notes that adding salt early enough will allow complete penetration of the bean, which improves flavor.
On the other hand, things typically added with salt -- particularly sugar and calcium-rich products -- tend to toughen beans (and the salt gets the blame). This toughening effect is most notable in baked-bean recipes using things like ketchup, molasses, and BBQ sauce. You can bake these beans for days, yet the beans will stay whole and firm. The actual mechanism for this effect is not clear; one hypothesis currently circulating seems to be that these products stabilize the cell-cell "glue" (e.g., Shirley Corriher says so on Good Eats "Pantry Raid III - Cool Beans", transcript online here), but I could not find any peer-reviewed study specifically verifying that hypothesis.
Best Answer
Per Harold McGee, in On Food and Cooking (page 86 of the 2004 edition), there is no truth to this common assertion.
McGee explains that the salt separates into ions, which cluster around the charged regions of the egg proteins, allowing them to get closer before being denatured because they don't repel each other. This causes them to bond together earlier, before they become unfurled and could form tighter (and thus tougher networks).
McGee concludes:
So salt them when you beat them, or in the pan, in practice it will make little difference compared to many other factors, such as the temperature and technique with which you cook them.