I see no evidence for the claim that the selection of help-worthy is often arbitrary. Anyway, I'll accept your example for the sake of the argument.

Of course, why shouldn't we help people who are second, third, or fourth born if they are at a systematic disadvantage according to robust data?

AFAIK, many societies have changed hereditary law over the past centuries to compensate for former advantages of first-borns in favour of other family members.