Then there would have been time to set the ship to self-destruct, so that Klingons, scavengers (like Orion pirates) or anyone else couldn't pick up a critical piece of the ship's systems?
I love Star Trek and want this show to do better than it has been doing so far, but the writing (especially in those first two episodes) left questions big enough to ram the 2009 Enterprise through.
Can you note a specific time where Starfleet self-destructed a ship for the principle of keeping general tech from someone else? All I can think of is the Stargazer which wasn't destroyed, and the Glenn which had the game changing tech on it and was in danger of being captured. Other ships that were self-destructed or threatened were generally the leading edge Constitutions or Galaxies or Sovereigns and/or when they were being actively taken over by enemies. The Shenzhou was an outdated ship.