It's the "dead" part that is the most problem. The goal is not to increase the number of voices the student hears, but to reduce them, so that only the present exists. The illusion of multiculturalism is not hard to overcome, as what they mostly mean is different foods, music, ways of dress. Fun stuff. Not too intellectually demanding. One can indeed learn something about other cultures by reading Zora Neal Hurston and Ida B Wells, and should. But they aren't very dead, not even a hundred years, and the cultures the write about still not so very far from ours. And even they, if I can tell aright from this distance, are not read for what is different about their lives but for what the student can pretend is "just the same," as illustrations that prejudice America now is really not that far from what they wrote about. Those two women would say otherwise, I have no doubt. They sang more than one note.
Female writers are few as one goes back in history, as are writers of color. Yet this is a feature, not a bug, as it becomes difficult to find anyone from the past who might whisper to the student that people thought otherwise than they do today. Let us talk about the prejudices they faced, children - just like today! Pay no attention to how their values and motivations were not quite the same as ours, because then we might learn something from them. We therefore have only moderns to draw from, people who drive cars, watch TV, go to restaurants, and get everything from markets. The amount of diversity is going to of necessity be quite limited.
Which is the point. Orwell believed that thought control would come via restrictions on language. He was close, but not right. By excising categories of writers and eras, students can be given the illusion of freedom. It is like Montessori kindergarten, where children are set down in a carefully-curated set of objects and given specific requirements about how they must move from one task to another and then told "You can do whatever you want!" Or the Philadelphia Mainline mother in the 1970s bringing her teenage daughter into the clothiers and saying "Navy blue. All wool. Whatever she wants."
Though modern academic Theory derives from Marxism, it differs sharply from anything written by Marx. What is shares is viewing everything through the lens of power. "Privilege," "subaltern voices," "postcolonialism" - these are mostly fancy synonyms for perceived power. They are mostly talking about the distribution of power in the present. Even when they dip into the past, it is usually the recent past, and framed in a way that the modern writer can shape the narrative and pretend to speak for those powerless others. Yet they get even this, the one thing they focus on, wrong to near opposite understanding. They and their group do not have the power they think they should. Therefore someone else must have it, and is holding it unfairly. Yet power is actually distributed among us in many ways, as I have written frequently.
Three great problems arise from this. First, by not understand what is actually going wrong, nothing they do is going to fix it in any way, leading to ongoing frustration and even fury. Fighting privilege, insisting on equity, and insisting that others listen to them will in twenty years bring about a situation - that is no better than what we have now. If not worse, for the second reason. Such a focus, being founded on resentment rather than justice and thus angry to its core, even among good people who are genuinely trying very hard to be kindly, will communicate anger and hatred and provoke anger and hatred. Thirdly, by cutting themselves off from the voices of the past, they will have nothing to fight back with. When encountering situations they do not quite understand they will only be able to project what they themselves think. They will remain at the mercy of demagogues* interpreting life for them.
*I hesitate to use the word "demagogues," as it is usually only uttered by those who are demagogues themselves. One should also do a self-check on that one.