The only reason illiberal values persist is because those who hold them know (or are confident) that they're not personally going to be victims of them.

You might be right, but I'm less sure of this.

Someone with more historical or anthropological knowledge than I is welcome to correct me, but I'm given to understand that many of those whom we would consider victims of an oppressive social system, actually support the system. (E.g., while woman's suffrage seems obvious now, there were many female anti-suffragists at the time.) It's likely that such sentiments would be nullified by a "knew more, thought faster, &c." extrapolation, but I don't want to be too confident about the output of an algorithm that is as yet entirely hypothetical.

Furthermore, the veil of ignorance has its own problems: what does it mean for someone to have possibly been someone else? To illustrate the problem, consider an argument that might be made by (our standard counterexample) a hypothetical agent who wants only to maximize the number of paperclips in the universe:

The only reason non-paperclip-maximizing values persist is because those who hold them know (or are confident) that they're not personally going to be victims of them (because they already know that they happened to have been born as humans rather than paperclip-maximizers).

---which does not seem convincing. Of course, humans in oppressed groups and humans in privileged groups are inexpressibly more similar to each other than humans are to paperclip-maximizers, but I still think this thought experiment highlights a methodological issue that proponents of a veil of ignorance would do well to address.