Can computer corrections make simple lenses look good?

Mathematically, if you know the exact transfer function that caused the blur, you apply the inverse transform, you will arrive back at the original image. (I.e, deconvolution, which is nothing new nor nothing magical).

That is the reason for them seeking to understand the lens’ point-spread. Understanding a function’s impulse response tells you a lot about the function behaves.

Blur doesn’t mean that information is lost – it only means that information is spread-out. In a purely academic example, if you apply a simple gaussian or spatial-averaging blur to an image, you can get the original image back from the blurry image just by applying the blur function’s inverse.

Of course, a lens’ blur characteristics are more complex than the simple academic examples, but it doesn’t mean the information is irrecoverably lost.