I add salt to pasta water in order to reduce the stickiness caused by starch. However, I've never seen potatoes stick together. Why add salt?
Salting the water in which you cook starches (pasta, rice, potato) is an effective way of enhancing the flavour of the finished product - boiling starches absorb salt well (which is why adding chunks of potato to an overall salty stew will lessen the apparent saltiness of the dish.
But salt does other things. When I am making roasted potatoes, I parboil them for 5 minutes before drying and roasting them in oil. if you divide them into two batches and boil one half in unsalted water and the other half in well salted water (1tbsp/2 quarts water), the salted potatoes will brown and crisp much better than the unsalted ones. I'm not sure why this is, but I would encourage you to try it because it's amazing to see.
First, as a physicist I would argue that:
-salt RISES the boiling point of water. Every student knows that.
-by osmosis, being the water salty results in a lower content of water in the potato. That is, the potato absorbs LESS water while cooking (there are some videos in YouTube showing this fact.) With less content of water, potatoes become crispier after roasting.
If you reduce the amount of water you use and increase the amount of salt, the result will be salt crusted potatoes, with added flavor and sweetness.
Pasta absorbs boiling water as it cooks, so the salted water actually seasons it. But whole unskinned potatoes absorb little if any water when they cook/boil, so they do not get seasoned. Although I have no data, I suspect that neither the small increase in boiling temperature nor the tiny bit of osmosis resulting from salting the water would be of much consequence. However, cut and/or peeled potatoes might indeed be seasoned somewhat, depending on how much cooking water they absorb.