The Shulchan Aruch addresses all of this. The point is that some taste particles may have wound up in the walls of the pot. As shishim is measured by volume, not mass, and volumes aren't necessarily additive (1 gallon water + 1 gallon alcohol = 1.96 gallons total), we can only play it safe if we assume there was a volume of milk/meat/non-kosher taste particles in the pot walls equivalent to the total volume of the metal of the pot. It is thus very rare to have 60 against such a volume.
(The one exception would be if I take a brand-new pot, pour in 1 cup of beef broth, and boil; then I pour it out and clean out the pot. Now I pour 62 cups of milk into the pot and boil. In this case, I know that there is no more than 1 cup total of meaty particles contained in the walls of this pot, so it is in fact batel. [Bonus points for discussion of other opinions on chan"an in this case.] But generally, pots have been used a lot, so we assume the volume of the walls to be entirely filled with flavor particles.)
This is why we have to resort to nat bar nat when cooking pareve soup in a dairy pot (for Sephardim anyway), as bitul beshishim is unlikely.
To answer your second question: In industrial applications we generally assume ben yomo; a company could easily do a dairy run and a non-dairy run in the same day. (If anything, they're very unlikely to let their machinery sit unused for a whole 24 hours!) So the "DE" potato soup is the industrial equivalent of if you boiled milk in a pot, washed it out, then an hour later boiled pareve potato soup -- the general guidance from kashrus agencies is you don't have to wait six hours, but don't eat it with meat!; this is exactly how the Ramah and Shach come out in this case.
(A true case of nat bar nat means the food is completely pareve; i.e. you can mix it with meat or milk.)
