Also, having the nameless Romulan die doesn't sound like much of a problem for Starfleet. He's a despicable enemy on an immoral mission, and letting him live would be a display of weakness! Dragging his corpse behind a shuttlecraft around and around Tomalak's Warbird is what the Romulan commander would actually expect, and there isn't a damn thing he could do about it...
It's only crucial for the characters themselves, not for the organization that they serve, whether the Romulan lives or dies. And Worf and Picard deal with the matter in a way that strengthens their standing in the show... But Beverly Crusher could probably brush up on her delivering-of-vital-information-in-time skills. Or is it just an unfortunate coincidence that Picard phones her to say "I have just spent five minutes groveling and pleading and losing my dignity over the issue of the prisoner's survival, now please let him die" at the exact
moment when the Romulan actually crocks it?