Depressing turnout by demoralizing constituencies that lean to the other side and, particularly on one side, outright voter suppression, is something that the rich (both independently and acting through the major parties) fund lavishly, so why wouldn't they get blame when turnout is low?
No, it doesn't. It lowers the threshold for dictating policy, and biases it to particular interests; that makes tyranny of those interests more likely, including when they command a bare majority (or even large minority) of support.
You don't fight tyranny of the majority by unequal representation; you fight tyranny of the majority with constitutional limits on what government can do at all, or by requirements for supermajorities or (as some state constitutions do) multiple time-separated votes (or both!) for particular kinds of action.
Crafting campaign finance laws in such a way that those with more wealth can disproportionally affect election outcomes is anti-democratic.
Voter suppression/disenfranchisement in the form of impediments to voter registration, voter ID laws, felon disenfranchisement, misinformation about voting process/procedures, closure of DMV offices, etc. are all anti-democratic tactics used by political parties to reduce/refuse voting access by constituents.
If a party can make voting inconvenient/inaccessible to a targeted population they can win electoral outcomes that do not match constituency desires.
Voter suppression is real. Voter suppression works.