Using as young as to talk about people who are young isn't unusual at all.
Generally speaking, if it sounds normal to say "Anne is young" then it will also sound normal to say "Anne is as young as Lucy."
Even in a qualified context it's fine. "Anne is young for her age—and Lucy is just as young as Anne."
One reason it sounds strange to use young rather than old in some cases is because the word old serves a dual purpose, while young does not.
We can talk about a one-year-old child, but it's not idiomatic to talk about a one-year-young child. So even though the child isn't old (but is actually young), the adjectival phrase that describes the child's age uses the word old.
As such, old is used to quantify an objective number of years. So, when we say that Anne is as old as Lucy, we mean that Anne has lived the same number of years as Lucy.
But when we say that Anne is as young as Lucy (when we would normally call neither of them young), we get a bit tripped up because young isn't used in that way. Instead, it's used to ascribe a quality to someone—that of youth. So hearing young used to describe years lived sounds strange.