It's also, possibly one of the few talking points that forces acknowledgement that those independent, unaffiliated, and unregistered voters exist and whose interests might matter towards the outcome of policy and/or elections.
On its own, it doesn't quite force the second half of that acknowledgement: The missing part is the "or else".
So far, the most charitable interpretation, if we disregard corruption for a moment, is that the party elite doesn't really see those interests because they have been too far removed from these voters for too long, if they've ever known it at all. Humble beginnings don't mean shit if you haven't lived humbly for the last few decades any more. So even in the best case, these people will struggle to actually comprehend. They also know that voters are faced with the choice between them and Republicans and can count on a chunk of people to vote just to avert the worst result. And they themselves aren't affected that badly by a potential defeat.
This disconnect is clearly visible in the shocked reactions to the "insurgency" of progressive politicians winning primaries: They don't know or don't want to admit what appeal those upstarts have that they don't, but at least they now realise that these other groups exist and matter.
Hence, "both sides bad" on its own is a criticism without a solution. It incites fatalism without rallying support for an alternative. Voting in primaries can have an effect, and if people genuinely don't want to vote D just to stop R in the general election, they should vote for some third party. Agreeing on a progressive candidate would help, but even without agreement, it would signal support for breaking out from that game of two.
(This also matters beyond the pure democratic mechanism: signalling that support can help other unhappy people to see that they're not alone and encourage them to join whatever form of resistance may emerge in their area. Even if votes might not change anything directly, they're a communication tool.)
A Roman satirist once remarked on the fact that the people were all too excited to celebrate a failed coup, but would have been just as excited to hail the new emperor. To paraphrase, they have given up oversight, and those whose votes once decided over offices and command of armies now only hope for "bread and circuses" (stable grain supply and public entertainment, basically). The full meaning is more complex, but the part that's relevant to me here is his contempt for the non-voters whose complacency led to a situation where they can no longer hope for more than bare necessities and a bit of distraction.
In that sense: Vote. Don't cede ground to those who want you to not vote. A voice that doesn't speak isn't heard. Even a "wasted" vote is better than silence.