If the "assumption" is so obvious and near-universal, why does Singer go on pompously to announce it.

Possibly for the same sorts of reasons that Eliezer wrote this big long thing to "restore a naïve view of truth", or that Nick Bostrom wrote this big long thing to explain why death is bad ... namely, that people have come up with all kinds of non-obvious, idiosyncratic rationalizations to justify the status-quo of starvation, ignorance, and death; that these rationalizations have, over the centuries, become cached thoughts; and that therefore getting back to "obvious and near-universal" basics is both desirable and nontrivial.