Straw alone wouldn't have enough nutrition unless it was used as a soilless medium for a hydroponic solution or maybe compost tea.
My folks used old 35 gallon galvanized trash cans (remember those?) with their bottoms rusted out, put compost in the bottom and planted 3 spuds. As the potato plants grew we gradually filled the cans with alternating layers of soil and compost never quite covering the foliage. It grew out the top in a riot. The cans had to be watered heavily each day.
At the end of the season we pushed the cans over and harvested 35-50 pounds from each. Sure beat digging potatoes out of the ground.
I've done the same here in the Arizona desert but in the winter garden. Summer is too brutal.