Well, doesn't that also imply that they also left the telescope?
Why would it imply that? They didn't evacuate the ship in the middle of a Klingon boarding action, nor in the middle of a pitched battle. They abandoned ship because they were hopelessly stranded and literally didn't have anything better to do.
Perhaps when they abandon ship, there's a ship-wide mechanism that disables critical components
Perhaps Uhura's miniskirt also doubles as a flotation device? No one ever said it wasn't, so we might as well speculate right?
It's not so much a matter of sanitizing a crash site but to prevent anyone from using particular devices, and one can imagine that taking place automatically as the crew abandons ship. That might not even mean recovery but simply disabling or using booby traps.
Neither of which Starfleet has ever bothered to do in the past. So why are you acting like it's a given that they would have done that to the Shenzhou? It's not standard procedure and never has been. There are reasons to think that it SHOULD be, but Starfleet evidently does not share that reasoning.
I mean, the Cardassians obviously do (Civil Defense) as do the Ferengi probably. But we can conclusively say that asset denial is not something Starfleet has ever really bothered with.
All I'm using is common sense. If the crew had the discipline to bring along a telescope of their dead commander (plus a container and a will with instructions to give them to the mutineer?), then they very likely had the discipline to simply disable a power core.
The power core was already disabled, and their ship was dead in the water (that is, in fact, the entire reason they abandoned ship in the first place). But Shenzhou is a starship with billions of different parts, and without knowing what the Klingons or anyone else might have been able to salvage and use, the only way to deny them those assets would be to blow up the entire ship.
Which, as I have pointed out, is not something Starfleet has ever done with its abandoned ships. Standard procedure is to just leave it floating in the debris field until someone (usually another ship) can swing by later and retrieve it.
Because the possibility of additional Starfleet vessels showing up to tow them home is a pretty strong one. Taking the lifeboats and hoofing it to a rallying point is a far more dangerous move, but it becomes worth it if they have no other alternative.
Or hours? Or given the level of damage, perhaps minutes?
The level of damage to the SHIP wouldn't affect the status of its emergency batteries, as that mostly depends on how much load you're putting on them. Suffice to say, they had at least as much time the Enteprise had Khan disabled the main energizer and auxiliary power. Per Spock, that is AT LEAST two hours, though Scotty's repairs probably took quite a bit less time than that.
Either way, that's two hours in which the crew had literally nothing better to do except count their dead, lick their wounds, and prepare to abandon ship. If a crew of 100 officers can't find time in two hours to pack their dead Captain's priceless family heirloom, I shudder to think how you think they'd manage to trigger a self destruct mechanism.