The author suggests that "The fear that multiple submissions would overwhelm the peer-review system lacks empirical evidence". Maybe it won't "overwhelm" it, but it will certainly add to the reviewing workload. Simply stated, if authors submit to N journals and each asks for 2 reviewers, that's 2N units of work (assuming they can get the reviewers), compared to 2 units of work.
But it may be worse than that, actually. I will not be much inclined to bother reviewing, if I know that the authors might pull their manuscript if another journal gives a green light quicker than the journal for which I have been asked to review.
The solution to a slow reviewing process is not to ask reviewers to do more of this unrewarded work.
Why can't the journals share reviewers? Once the reviews are in, the editors decide if they want the paper in their journal, and if more than one does, the authors get to pick. Obviously it would be a bit more complicated with revisions, etc. but it would be an improvement over the current system.
But it may be worse than that, actually. I will not be much inclined to bother reviewing, if I know that the authors might pull their manuscript if another journal gives a green light quicker than the journal for which I have been asked to review.
The solution to a slow reviewing process is not to ask reviewers to do more of this unrewarded work.