Are some people really that desperate to "see themselves" in the entertainment they watch?
It's not so much that they want to "see themselves" in the entertainment they watch. As you have noted, it's primarily middle-class white kids who are demanding these things.
No, it's the power to make you change what you're doing, in any way, that they enjoy. It's the ability to claim empathy while expressing the exact opposite that they enjoy.
For hundreds of years storytelling has been about deliberately depicting people different from those who are hearing the story, ideologically, personally, in any myriad of ways, because the narrative empathy is inherent in healthy people. It's notable that decreases in real racism and real sexism happened when more exposure to people who possesses traits as part of being a well-rounded character are presented in media to populations. (Simultaneously, we also find brand-new ways to hate other people and things to hate them for, but that's the nature of man.)
The Woke don't want that. They pronounce the words but they don't believe them. And I have an increasing belief that this is because they don't have the ability to express narrative empathy. They literally cannot see someone who varies from them self as an empathetic being. And that is an attitude which has been cultivated rather than curtailed.
Ultimately, they just want to control you because they don't think of you as a person "like they are." And then they project that attitude on to you because you're different than they are.