I'm not sure this question has a clear answer, but I'll give it a shot. First, poitin is more like American moonshine than vodka. Vodka is distilled to a much higher proof, usually on a column still, which cleans off most of the taste markers of the original mash. It takes a practiced palate to tell the mash differences between high quality vodkas. Poitin, on the other hand, is made on pot stills and distilled to a much lower proof, leaving in far more of the mash markers. It is essentially unaged Irish Whiskey. In fact, the lack of aging is one of the criteria for the Geographical Indication for Irish poitin, which was released in 2015.

Poitin being made from potatoes is also somewhat of a misdirect (I'd guess it's decades old folklore gone awry). True, poitin has been made from potatoes in the past. Like moonshine, most backyard distillers will make their product from anything they can get their hands on. Originally poitin was grain-based, just like its legal brother. And most poitins being legally made today are grain based as well (eg Teeling)

In 1661, the British Crown created a a customs and excise tax on Irish whiskey in part to help pay for their military presence within the country. This tax was largely ineffective, but is the reason for the split between parliamentary (legal) whiskey and poitin (moonshine). Both were unaged at the time. In fact, when the Crown switched over to taxing the still itself rather than the volume of its output over a century later, the quality of legal whiskey plummeted and poitin became the superior drink. I could keep going on the history of Irish whiskey, but those are the basics on how the split was born between the two products.

Now, I have some guesswork in the realm of why potatoes never took off as a staple for Irish spirits. Grain-based whiskey already had a rich history by the time potatoes entered the scene in the late 16th. From what I've read, potatoes weren't cultivated on a large scale anywhere in Europe until the 19th century. They were a garden crop, grown and eaten by the poorest members of society, prized for their nutritional value and high yield. There was no scalable source for large whiskey producers. However, the subsistence farmer with a still in his backyard could certainly use his excess potatoes to make some adequate poitin at the end of the season.

This is definitely some guesswork, but there has also always been a whiskey producing rivalry between Scotland and Ireland. There are centuries-held debates on who created the first dram of proper whiskey, and whose production methods are superior. I would hazard a guess that whiskey producers in Ireland wouldn't dream of using anything but malted and unmalted barley because that was the proper way to make the stuff, and because the Scots would never let them hear the end of it.