What follows is an extended comment on the proposal of pre-print peer review by Sabine Hossenfelder.
She suggests, inter alia, that the authors pay a submission fee for each paper and the referees get awards for their reports. But is the fees-related part of the proposal necessary at all? Perhaps the universities could donate some funds (as they already do for the arXiv) to get the thing going, and major professional societies (APS, AMS, etc.) could chime in too (and the authors can donate on a purely voluntary basis). To replace the awards for refereeing and the author fees one could use some kind of “points” (pretty much like the reputation points on the stackexchange sites): submission of the first paper is free, and the next ones are “paid” by the points obtained from refereeing. There could be some points gained for any report and extra points if the author(s) like the report (and express this by marking it as “favorite”).
UPDATE: another interesting and very detailed proposal on an alternative peer review model is Open Peer Review by a Selected-Papers Network by Chris Lee.