Isn't it possible to computationally counter the effects of diffraction and distortion?

Generally speaking yes! That's what companies do that create masks for lithography so that the structures the manufacturers can create are smaller than the wavelength they use in the process. (See https://en.m.wikipedia.org/wiki/Computational_lithography). The article states that generally this is rather computationally expensive and I would wager that an analogous concept would be too. Perhaps a Neural Network could be trained to infer corrections and maybe that would be feasible then but maybe someone else with more experience in the field can elaborate on that.

Neural networks suffer from provability issues, you don't want to make a multi million dollar mask set only to find out your ConvNets were hallucinating. There are more standard computational lithography techniques such as OPC, RET and inverse lithography.

With that being said, there's been some work done:

https://ieeexplore.ieee.org/document/5726499/

https://www.spiedigitallibrary.org/conference-proceedings-of...

http://iopscience.iop.org/article/10.1088/2040-8978/12/4/045...

https://www.google.com/url?sa=t&source=web&rct=j&url=http://...

Non-mobline link:

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

Especially when you have a predistortion image from the frontmost sensor, and I would imagine that the diffraction would remain constant between photos - manufacture differences would presumably mean each sensor would need to be calibrated, but with the multiple sensors, it seems quite possible that could be done by the consumer.

They say the answer is "yes". It's even nominally offered as a feature in, e.g. Canon's RAW processing tool (called "DLO")

Unfortunately, in practice it seems to behave more like smart sharpening than a discrete reverse convolution math op.