"Prevent the enemy from salvaging usable parts" has never been a priority for Starfleet.To find the ship before the Romulans do. Salvage it if possible, destroy it if necessary.
The Shenzhou fits two scenarios. The possibility of destroying her to prevent the enemy from salvaging usable parts
Note the bolded part here: there are MANY reasons why Starfleet might destroy a starship to keep the enemy from getting it. "They might salvage some part of it" is not one of those reasons and never has been.
It is illogical to perform an action simply because you cannot think of a reason NOT to. If such action serves no constructive purpose, you are better off refraining from taking it.The last part of your question is where the devil is. Was there a good reason not to initiate it?
Obviously there were, as you yourself keep pointing out (e.g. the dilithium processor and whatever else might have been aboard that Starfleet could have used for parts).To answer 'yes' to this means that there were indeed resources worth keeping 'afloat'
But Starfleet isn't going to destroy the ship just to keep the KLINGONS from salvaging it, not when they still have a chance to recover it themselves. IF Shenzhou had still been warp capable and IF there was actual reason to believe that the Klingons were likely to board the ship and fly away with it, THEN they would have destroyed it to keep that from happening, or at least sabotaged the engines so the ship could no longer move.
But blowing up the ship just to keep desperate starving Klingons from scavenging spare parts? That's not their MO. Hell, Starfleet has been known to DELIBERATELY aid its enemies when they fall that far off the wagon. Those are the high-minded principals Kirk was talking about in "Corbomite Maneuver", it's the thing that compells the Enterprise to render aid to a Romulan warbird in "Timescape" and it is PRECISELY the reason why James "Let them die!" Kirk surrenders to Kronos-1 and then beams aboard to render aid instead of just opening fire on an obviously battered cruiser to protect himself and his crew.
"Valuable" here is relative, though. Shenzhou's processor is valuable to Voq because he's desperate and starving. It's worthless to Kol, however, who never gives it a second look and actually doesn't care about it at all except that it gives him an opportunity to finally buy off Voq's crew with a giant bucket of KFC.If that was the mindset then it is an acknowledgement that something you know to be valuable is left for the enemy to take advantage of as well.
The chicken ended up being ALOT more valuable to Voq's crew than the dilithium processor.
Lest we get into another round of war stories, there's this great annecdote from Paul Tibbets about getting fished out of the sea by some islanders who were trying to figure out whether to sell him to the Japanese or the American forces in Guadalcanal. The Americans apparently made them the better offer, leading Tibbets to remark "Apparently my government believes my life is worth exactly one ten-pound sack of rice."