>'Distortion' is actually missing data, and you can't bring forward something that simply isn't there.
Well that's true, but not by any means the only definition. Distortion can also be caused by too
much data, and not all of it is removable by any means. Basically, it's mixed in with what's wanted - and like cakes, you can't exactly 'unbake' them after the event.
The real issue is that in a system that by absolute necessity has to be automated (far too much variable data to be analysed by hand), the automated system has no real means of identifying what's wanted and what isn't - with a few relatively minor exceptions. In order to remove a component in this scenario, it has to be capable of isolation in an electrical sense - so for instance, with a stereo signal, it's not impossible to establish what portion of it is at any given position in the stereo field, and remove just what's at that position. Which means that something like a vocal, which is generally in a single fixed place, can be operated on with a reasonable degree of success (although anything else in that position will also be affected). But the same principle, when applied to something like reverb, simply won't work - because reverb is invariably decorrelated, and occurs all over the soundfield. And because it can't be isolated, it can't be either treated or removed.
There are various things that
may in the future be possible, but they are going to require massive amounts of processing, because at the very least multiple tracking FFT systems will be required.