>Basically: why hasn't someone come out with a camera with a junky single-piece lens and a fancy image processing backend and won the market?

that's what phone cameras are...

And a lot of lens aberrations not correctable robustly. LCA is basically impossible to correct, field curvature is impossible to correct, bokeh quality is impossible to correct (within reason), wide depth of field is impossible to correct, dynamic range is impossible to correct (without bracketing), coma is impossible to correct, flaring is impossible to correct and the list goes on.