Such tools (e.g. Photoshop) already ship with a database for lens correction of most lenses from the large manufacturers. Things like chromatic abberation, vignetting etc. can be done automatically. For some common lens problems such as geometric distortion, I'd say the correction is so good that I wouldn't consider it to be a problem when buying a lens any more, whereas it was one of the larger problems with zoom lenses before.
As far as I understand this method just requires the PSF data for different settings to be shipped as well (at different apertures/focal lengths), and Photoshop could do the same thing using this method.
Abberations in a poor lens comes from two factors: 1) design flaw/compromise and 2) sample variation. If you have a lens profile in Photoshop with PSF data it can only correct for the problems inherent in the design of the lens (1), not problems due to variations in manufacturing or lens damage problems.
I think it depends how much two lenses of the same model/type are different: maybe you could have presets for common lenses and/or finetune the system for your own one doing some calibration shots.
I wouldn't be surprised that you could make the convex optimization algorithm independent of the lens. That would just be prior information for the algorithm which you won't necessarily need.
