It's essentially like "cracking" a password when you have its hash and know the hashing algorithm. You don't have to know how to reverse the blur, you just need to know how to do it the normal way, you can then essentially brute force through all possible characters one at a time to see if it looks the same after applying the blur.

Thinking about this, adding randomness to the blurring would likely help.

Or far more simply, just mask the sensitive data with a single color which is impossible to reverse (for rasterized images, this is not a good idea for PDFs which tend to maintain the text "hidden" underneath).

If, however, one just blindly uses the (generalized)inverse of the point-spread function, then you are absolutely right for the common point spread functions that we encounter in practice.

One way to deal with this is to cut off frequencies where the signal to noise in that frequency bin is poor. This however requires some knowledge about the spectrum of the noise and signal. Weiner filter uses that knowledge to work out an optimal filter.

https://en.wikipedia.org/wiki/Wiener_deconvolution

If one doesn't know about the statistics of the noise, not about the point-spread function then it gets harder and you are in the territory of blind deconvolution.