If your education system is managed by politicians, then 'woke' is a stupid thing to invoke. There is simply just different political perspectives on what is necessary. You referencing 'woke' in a negative light simply betrays that you are in a different political camp to those you disagree with and are unable or unwilling to strike out for a middle ground of acceptable materials.
When I'm referencing 'building blocks' I'm not referencing Odysseus, I'm referencing basic grammar, reading, writing, math etc... And realistically, that can be adequately taught with the most 'woke' curriculum you could think of - or the opposite libertarian equivalent. In fact, I think you're arguing something that isn't really important until high school when students should be taught about different types of source material and are increasingly specialising their fields of interest (at which point your 'woke' comment becomes irrelevant) or university when students are developing their own theses based on their own research. If students are actively prevented from finding their own source material they need at this point, you've got a problem, otherwise I think you're describing a storm in a tea cup.