The poem opens with three odd images: sitting in a cradle, burning coal in the street, talking with an alabaster sage. Each one feels slightly wrong or out of place. A cradle is for babies, coal belongs in a grate rather than a roadway, and an alabaster sage is a statue, so the conversation can only be one-sided. The opening question, "who would" do these things, suggests that no sensible person would.
Then comes a different kind of image: a poor man, complaining of his hardship, sending his son to sea. That seems to be a desperate choice, putting the child in danger to ease the family's trouble. The final lines step back and comment, saying how easily people forget time.
The speaker sounds wry and a little weary, more observing than angry. The poem seems to suggest that people act against their own good because they lose sight of time, whether that means age, consequence or the future. The mood is quiet, puzzled and faintly sad, and the title's irony adds to it.