Except that there was a plot point and reason. Worf felt that he was unable to provide a decent life for Alexander on the Enterprise. He had no experience being a parent and had only just shortly prior had discovered he was a parent to begin with.
Your assertion that Worf "punked out" is wrongheaded and shortsighted. Are you sure you're not just imposing what YOU would do in his place? Because that's one thing, but it's another to ascribe such a negative connotation to Worf's actions, when they were perfectly understandable at the time.
Why don't Picard or the others talk him out of it? Probably because it was none of their goddamn business. I'm not saying it was the right choice, but it was a legitimate story choice for the character to make precisely because it does make us debate it and possibly even be unhappy about it, the same way it was a perfectly legitimate choice for Worf to not donate the needed blood so that the dying Romulan in "The Enemy" could be saved.
Besides, as I mentioned before, it's a moot point since we all know less than a year later, Alexander wound up coming to live with Worf on the Enterprise anyway.
Worf is a character rife with contradictions, the contradictions in his personality are pointed out often, especially by Troi. To accept Worf as a compelling character is to accept these contradictions as part of the narrative. He's not a real person. I think you are supposed to be disappointed with his decision to send Alexander away.
...persona: brave, honorable, dutiful.
Pretty one-dimensional, and not very interesting.
The fact that you are disappointed in the character and not the writers indicates that this was an effective plot point.
Exactly so.