Could future airplanes use rockets to recover plane and/or prevent crash landings?
They could but there really is no reason to do so. Most aircraft glide just fine if they lose all engine thrust and are perfectly controllable in such situations (provided they can actuate the control surfaces). As for the situation you propose there are a few issues with it, 

First off, rocket fuel is not jet fuel and can't just be burned in the same way. 

The JATO engines are a bit different than the rocket assist that Space-X is using (although the principal is similar). For takeoff the Jato engines help add to the totally available thrust and allow the plane to get off the ground in a shorter distance. The rockets are (I believe) single use and provide a very quick burst of thrust.  

As for the loss of control this depends on what causes the loss of control and how the rockets are affixed to the airframe. In the case of the Alaska airlines flight you reference the jack screw forced the tail into a position and prevented it from moving, this put the plane in an unrecoverable dive that would only be exacerbated by rocket engines unless you could control the angle at which they were pointed. Again in the outlined case you would need to be able to counteract the full surface deflection of a control surface. In essence you would need the kind of thrust control that space ships have used over the years.   

Now to answer the broad question of "could rocket thrusters be used to bring a disabled aircraft down softly" the short answer is yes. They could be added for such a task but the toll they take on the plane would make it a hard sell to the airlines. In short the use case is small and the added weight cuts into the profitability of the flight (you need a lot of jet fuel and heavy thrusters to pull this off). On top of all that the system would have to be built and certified for use, a task that should not be taken lightly. In the end you get a safety system that has a small use case and a big impact on the aircraft. Perhaps the best thing airplanes can learn from space craft landings is the use of parachutes.   

The last and somewhat debatable point (common to all safety systems) is when do you actually turn it on? What is your definition of unrecoverable (yes this varies)? Cirrus teaches people to basically always pull the chute in an emergency. Are you going to teach pilots to to always trigger this rocket decent system even if the plane may be recoverable? What if you run out of fuel before getting to the ground and now you are to low to recover from the rocket assisted decent?