In Star Trek: Into Darkness, why is the warp core required to use thrusters?

In the prime Star Trek universe (TV series), the warp core is not required to power the vessel as ships can go without a warp core with functional impulse engines, thrusters, life support, and the list can go on - however the warp drive is inoperative without the warp core. Sulu states in Star Trek: Into Darkness that they need the warp core online to escape the atmosphere, I can't remember the exact quote but it was along those lines.

Since when did the warp core power all the ship, if so why would they add in an eject warp core function which is similar to a self-destruct in Star Trek: Into Darkness. Supposedly according to the film without the warp core you have no power, and life support requires power - you're just sentencing the crew to death.

I believe I am right to presume that the power of the warp core can be tied into other ship systems, especially the shields to reinforce them which is seen in TNG.

I understand this is considered an alternate universe, but the universe only became alternate at the point in time when Spock's ship entered the past in 2009.

Could someone clarify why the warp core was required to power the thrusters to escape falling into Earth's atmosphere (which is another continuity error as the clouds are in the atmosphere)?