After reading the paper, I have the impression that your headline focussing on rRNA depletion is very misleading, given the data. There is also bias in poly-A selection. Fig. 4B would suggest that the variation in coverage is even higher in poly-A selected samples than in rRNA depletion, because poly-A shows a much heavier tail. And the effect size is larger (Fig. 4C). On the other hand, if the variance in coverage in poly-A selection is only due to the 3' bias, then poly-A selection would gain an upper hand, because there are protocols with much less 3' bias available.
The other sources of variability (random priming and "sequencing-specific molecular biology common to all libraries") are always the same between the two methods.
The good thing is that even the "high, unpredictable coverage" (hunc) regions are reproducible between samples, so its a systematic error which should not affect differential expression analysis.
I assumed Ribo-zero has off-targets but I haven't realized it has such a tremendous effect. For bacteria, where ~90% of RNA is rRNA and no poly-A to select this issue is very big, are there any other solutions (other than sequencing ten times deeper)?