What is the usefulness of approximating an optimal decision rule that close enough to steadystate in RBC model? I'm reading understanding real business cycle by Plosser.

Here's my crude understanding: For a RBC model, the FOCs of lagrangian together with transversality condition usually forms a nonlinear difference equations system. The standard way of solving this system is by linearization in the neighbourhood of steadystate,  solve this problem as a linear difference equations system.

What insight can we get from this solution, except for gaining  some knowledge of whether the steadystate is locally stable?
Side note: This is one way of solving it - the alternative would be formulating a Bellman equation and iterating on that.

If you assume that the real economy is on or sufficiently close to the steady state, you can also infer about responses to shocks. That is, you can look at the impulse response functions to a change in whatever interests you, and see how the model economy changes. Arguing that we're close enough to that steady state will allow you to see how the economy responds to certain shocks.

Also, in general, you can simulate the economy with (for example TFP) shocks, and look whether the simulated economy looks similar to the real economy. Using this comparison you could judge the model.

This needs arguing that we are close to the steady state - or that convergence happens really fast. Generally, the growth literature around Solow has provided arguments for this.

But your argument is very present in most extensions of the basic RBC model: especially when it is important how close we are to the steady state - when models are more nonlinear. There have been many papers showing that this is the case for standard Neo Keynesian extensions of the RBC model.