Why is voter turn-out the relevant metric? You are implicitly assuming that increasing voter turn-out is a worthy goal in and of itself, and I am not sure why. Is it important to you that each voter feel involved, or that they are responsible for their representatives, or do you believe that an increase in the number of voters would improve policies and outcomes? I would support an attempt to increase voter turn-out if it would improve policies and outcomes, but there is little evidence of this; in fact, the current evidence shows that current voters are better informed and more intelligent than eligible non-voters.[1] Before you accuse me of being an anti-democratic autocrat or something of that sort, please keep in mind that I am not advocating the abolishment of elections, that I used to agree with you (but was persuaded to change my mind), and have voted at every election I am eligible for since reaching the age of majority.
The ethical case for democracy rests not on whether democracy leads to optimal policies and outcomes (which is ridiculous), but on the degree to which it includes individuals in the politics of the state exercise of power over them. The state necessarily has power over individuals, and the ethical basis for the use of that power declines to the extent that the state excludes people from participation in political decisions. It erodes the consent of the governed. The core injustice of things like poll taxes and grandfather clauses is not that they led directly to suboptimal policies, but that they disenfranchised black voters, which is what led to policies that the white supremacists considered optimal.
Voter turn-out indicates that information about platforms is passing from politicians to voters, and information about preferences is passing from voters to politicians. Low voter turn-out has tended to co-occur with the managerial turn of politics, in which no party or candidate offers any substantial choice to even the most enthusiastically civic subset of the population.
Essentially, low voter turnout is a correlated symptom of de-facto oligarchy.
[1] https://en.wikipedia.org/wiki/The_Myth_of_the_Rational_Voter