At industrial scale, surely they recover that copper from the etching fluid?

Yes, but this costs pales in the cost of redoing in case of problems with side-etching and the overall tightened manufacturing constraints.

And yes, they get to recover the copper, at the very least to make treatment easier for discarding (copper is a very bad pollutant). But not only there's a cost, this is dealt with by waste treatment companies that will at most use the copper value to recoup some of the cost of the treatment.