I do not deny that you can sharpen blurry photos of high-signal-to-noise scenes, e.g. deconvolution with a known point spread function.
The situation is different in the case of dim objects, which is frequently the case in interesting astronomical photos. If there are three noise photoelectrons in each pixel with a Poisson distribution, and a dim object would contribute only six additional photoelectrons, it makes a lot of difference whether those few additional signal photons are spread among a dozen pixels or only one - are those 6 signal electrons spread among ~36 noise electrons, or ~3? You don't know which ones are noise, or even how many are noise, except on average. And when there's only one picture, there's nothing to average.
I'm not denying the Hubble correction was necessary.