I never thought of it that way. For me Laplace is all about region of convergence and representing things like the Dirac Delta function in a way that’s easy to

I never thought of it that way. For me Laplace is all about region of convergence and representing things like the Dirac Delta function in a way that’s easy to manipulate. Basically the video ignores the idea that the X(w) integral may not exist. It doesn’t for many x(t). I don’t want to type a book, but basically the X(s) integral exists (where it does is called the region of convergence) for many more x(t), so there are classes of functions which can now be analyzed where with just Fourier, they could not be. The other thing is delta functions. With Fourier they are a pain but with Laplace they are a breeze. This is especially important if you want to mathematically model how the control system will respond to a jolt or impulse. I always figured that is why control engineers use Laplace.