If an engine fails in a passenger airplane, why can't it have movable rocket thrusters in the wings to help safely land the airplane?
Any time the question is "why don't we have...", the answer is almost certainly in the trade-off between weight, maintenance cost, fuel cost, & utility. If it weighs a lot, needs maintenance, burns fuel, and will only be useful once a decade, then it just is not productive.
Putting rocket thrusters on a plane will be heavy, meaning fewer passengers, or less fuel or cargo on board. All that extra weight has to be flown around, requiring fuel. They would need regular maintenance checks, which is another cost. And they would only be useful very, very infrequently (on most planes... never).
So, safety issues completely aside*, it is just impossible to justify adding new equipment for a once-in-a-lifetime scenario, which can be better managed with good maintenance, good training, and good planning.
*Safety issues are a big deal with rockets. Rockets are a controlled explosion. What happens if that explosion is not controlled? What happens if the rockets are triggered by accident, or blow up all at once? Even if rockets passed all the tests of utility vs. costs, they would still increase risks to the plane, rather than decreasing it.
"Movable rocket thrusters," regardless of propulsion, are used for thrust vectoring, AKA maneuvering, not forward motion.
If you're talking about something like an emergency JATO rocket, then the reason is because very, very few accidents happen strictly because of engine failure. Most engine failures (notwithstanding US Airways Flight 1549) happen at an altitude where the plane can pick a safe landing spot, and glide to the runway.
The advantage of rocket thrusters over conventional aerodynamic control surfaces is that they work in space. This is not a factor for commercial airliners, but some research aircraft designed for very high altitude operation, such as the North American X15 have used fixed rocket thrusters in addition to the conventional movable wing and tail surfaces. The use of such a system in a commercial aircraft would in itself pose major safety issues, because of the highly reactive nature of the propellants used in these systems, such as concentrated hydrogen peroxide (HTP).
The Boeing 727 was certified with a rocket-assist system as an available option, in order to meet one-engine-inoperative climb gradient requirements for operation at extremely hot/high airports. It was only ever selected for purchase by Mexicana airlines, and was delivered on 12 aircraft. You can find videos of it being tested on Youtube.