this approach would end up shuffling money around within the community of researchers

Would it necessarily? Aren't publication costs normally paid through the institution? If reviewers are paid, they could be paid directly.

It would be a very interesting change to the current incentive structure for academics. It would probably soften the tone of reviews up a bit and raise their quality, since reviewers would want to be perceived as high-quality by the editor to get solicited more often. My opinion is that this change would definitely be for the good.