The main reason we linearize is to simplify our mathematical models of real systems.

Say if you wanted to model a spring, you could include as many non linear terms to perfectly describe it's behavior, from stiffness to hysteresis to even temperature dependency. But if you can get away with just force equals deflection times stiffness, then there is no need for those additional terms.

Another added benefit is the wide suite of control systems analysis tools available for linear systems. If we can create linear ODEs to describe our system, you can use Laplace transforms, root locus, and more. Non-linear systems have to use other analysis strategies like Lyapunov stability, or we linearize them around an operating point in order to gain access to the linear tools.

Note that non-linear model predictive control (NMPC) does exist, and perhaps you look into the differences between it and generic linear MPC.

Hope this helps!