It’s not that the school would be uninterested in CS students but rather that there is a voluminous amount of them in comparison to most other majors.
You can see at Oxford the admission rates and the breakdowns for each and every major. There are far more applicants for CS than there are for Classics for instance. Filling multiple buckets is not really relevant here though I will say that it’s likely far more of a must for a CS student or it might be that the CS student will have a higher need to score a 1 in some category than it would be for a Classics student though filling multiple buckets may be a must for both. I do realize that Harvard and Oxford are not the same but the point is that intended majors likely do have some impact even if it’s an unconscious bias when reviewing essays.