Technically, no, they did not come up with this thought on their own. It's been heavily propagandized that 'voting does no good, so just stay home". I just want to point that out as it's an active attack on American voters.
People that are actually leftist don't vote because there's nobody that represents them. Most Democrat politicians are centrist.
Joe Average the Trump voter got to be the way they are from a "grooming" process of some kind.
Who would Trump have ever have picked up something like that from?
But it’s of course a hellishly complex problem
On the seemingly rare occasions that a democrat gets into the oval office, they spend most of their time on social/environmental issues that extend to all voters, but are fought at every turn. We desperately need a reformed political system. The only way that will happen is if the American voting public will get off their cans and put forth the effort to learn civics and then realize that their opinions must be tempered with reason.