Roughly 125 million people voted in the last presidential election. Had I been among them, I'd therefore have had roughly 1/125,000,000 of a say in who gained the office. Perhaps, to a homeopath, such a marvelous dilution of political power might leave something meaningful in its wake. Not being a homeopath myself, I find it somewhat less than compelling.
I fail to see how resignation in the face of inevitable powerlessness can be anything other than healthy. "How our society governs itself" is a subject over which very few people have, or might gain, any sort of influence; not being one of those people, and having neither desire nor reasonable prospect of joining their ranks, the profligate expenditure of mental and physical effort, to say nothing of precious and irreplaceable time, to pursue the meaningless self-appellation of "good citizenship", strikes me as falling well within the realm of foolishness.
Local politics, depending on where one happens to live, may well present a more worthwhile prospect. In my own case, and being that I live in Baltimore -- a city whose corruption is almost as famous as it is nigh-boundless -- I see little more reason to involve myself on the local level than on the national. Those of a temperament for politics, and who find themselves living in places where local politics are other than an Augean stable of gerrymandering and nest-feathering, might be well advised to involve themselves.