I would distinguish between "the left" as a political persuasion and as a political movement, and between "the left" and "liberalism." Both versions of "the left" could further split into "left progressivism" and "left socialism." Or again, as "Progressives" and "Socialists" (or Communists). "Progressives" in my ontology are "left liberals" (as opposed to "right liberals/libertarians").

By "the left" do you mean "socialism" or "progressivism?" If socialism, then both as a political persuasion and political movement I agree that "the left" "hates" the Democratic party. For one, the Democratic party is not socialist. Two, they compete for mindshare and the socialists always lose. I did not bring up the "left/right" dichotomy in my comments and don't believe they are that helpful in the current context. That said, the socialists don't really matter. Socialists don't/can't/won't/shouldn't hold power so their only function is as a faction within the broader "left coalition" that has broken down since the 1990s when global liberalism reached its apex. That coalition is dominated by "left liberals" (aka Progressives). These are not all that different teleologically from Communists, but seek to push forward a type of Whig history. The representative expression of this Whig history is Obama's "The arc of the universe is long, but it bends towards justice." Sometimes, it doesn't bend fast enough and has to be bent by technocratic governance. And this can't be limited to the borders of a polity or nation, but logically requires a global scope. It is both interesting and convenient that such an ideology happens to provide cover for the administrative actions of global empire. It would be hard to convince the individual people to act against their better judgment. Much better if they believe they are a force for good. Hence the role of indoctrination towards ideological conviction. You see the effect when this fails while the government persists in the later stages of Soviet and Communist governance. The people just didn't believe it anymore. If interested, you can read a sociological study of this effect in Timur Kuran's "Private Truths, Public Lies".

Nobody is "cunning enough to come up with a whole nefarious plan to indoctrinate the kids." Holding to such formulations is obtuse and a trivial form of casuistry. Ideology and its supporting indoctrination programs are emergent in the modern era. That said, plenty of past Propaganda Ministers have existed who did take an active role in managing popular opinion. They don't call themselves that anymore, but they still exist. (Interesting books have been written on the topic[0].) In the modern context, propaganda may seem subtle until some kind of crisis occurs when all points converge and you get those hilarious memes of all news anchors somberly enacting the same exact text at the same moment. It is at those times that one sees behind the arras and understands that "news" is not organic nor is it independent. Editorial boards collude regularly to shape public opinion. (I would call it a subtler version of Pravda but people who lived under Eastern European propaganda have scoffed at the heavy-handedness of our version compared to the actual Soviet programs.) The breakdown of this function/ability is one of the more interesting phenomena of our current times.

All that is to say that the process of indoctrination is not all that mysterious, but its conspiratorial aspects, while real, get too much attention imho.

[0] For examples, see Walter Lippman's "Public Opinion", Edward Bernays' "Propaganda", Noam Chomsky's "Manufacturing Consent", Jacques Ellul's "Propaganda", Sheldon Wolin's "Democracy Incorporated", Martin Gurri's "The Revolt of the Public", etc...