Vodka by definition is a flavorless distilled alcohol, retaining any of the organoleptic properties of the grain or potato could be considered as ruining the end product.
Potatoes are a good source of starch, but brewers yeast has a limited ability to break down starch into usable fuel; its preferred fuel sources are relatively simple sugars like mono and disaccharides. In order to efficiently convert the starch in potatoes to sugar the potatoes must first be boiled so that the starches gelate. Once gelated, the potatoes are then Mashed-in with malted barley or wheat at a temperature around 150˚F so that the diastatic enzymes can break those starches into the sugars that yeast likes to eat. These same steps are used when making vodka from non-malted grains such as corn (maize).
Boiling the potatoes also helps reduce the number of surface microbes that could end up influencing the final product. Bacteria and wild yeast strains can lead to moldy, grassy, sour, and other unpleasant flavors that may necessitate multiple distillations to remove.
Making a mash of raw, peeled potato would likely yield something closer to a sourdough starter with a mix a naturally occurring yeasts and bacteria producing a small amount of alcohol along with acetic and lactic acids, as well as other compounds.