Convolution smooths out functions. If you convolve any function with a Gaussian kernel, you get a C^infinity function (a function that has continuous derivatives of arbitrary order).

This anti-blurring effect would attempt to find for a given function f another function g so that g convolved with a Gaussian kernel is f. But if f is discontinuous no such function exists.

This is not just academic. Letters on a screen are discontinuous functions.

You could say that a certain amount of smoothness is tolerated. Or that all signals are discretized anyway, so the whole concept of continuity is mathematical non-sense.

So, what I provided is just heuristics, is not a solid proof. It's still in principle possible to produce such a anti-blurring algorithm, I just find it highly unlikely, I would not invest much time in it.