It's because the right benefits from low turnout. The left, representing the interests of the proletarian majority, benefits from large turnout. The Democratic party, a center left or center right party depending on who you talk to, has co-opted the left voter base and thereby depends on higher turnout during general elections. As a centrist party, they intentionally suppress turnout during primary elections (e.g. by not advertising the date in my community) to restrict ideological choices.