(I don't know anything about YC applications but) Because it's a useful context in evaluating the people. For example, how low quality certain aspects of the application could be perceived might depend on the person's age -- one being that a 22-year-old isn't going to have much of a resume. Also, if somebody makes certain kinds of mistakes, it's less of a red flag if they're in their early 20's, than if they're 40 and should know better.
The logic you just proposed is actually illegal in the states when it comes to job applicants, because it disproportionally discriminates against some candidates based on their age.
This is true for employers when considering applicants for a job (as you stated); but, as far as I am aware, YC does not employ any of their applicants directly. Since YC is a private funding group, the equal opportunity protections do not apply to their seed fund applicants. So this is more of an ethical issue than a legal one.
YC makes investments. Startups and their founders are not employees of YC. You are allowed to know the age(s) of individuals that own companies you wish to invest in.
Actually as mentioned it's illegal for employment, not investment, and also, my suggested line of reasoning would not be illegal, even under employment law. (It's not illegal to interpret a blank resume of a 45 year old in a more negative light than a blank resume of an 18 year old.)
Because they discriminate based on age. If you are older, you are expected to have done more. This is legal in investments.