If by "open" you mean that the paper is there and people just voluntarily choose to review it, rather than having some top-down coordinated assignment process,

If by "open" you mean that the paper is there and people just voluntarily choose to review it, rather than having some top-down coordinated assignment process, the problem is that papers by the superstars would get hundreds of reviews while papers from unknown labs would get zero. You could of course make it double blind, but that seems hard to enforce in practice in such an open setup, and still, hyped papers in fashionable topics would get many reviews while papers that are hardcore theoretical, in an underdog domain, etc. would get zero. Finally, it also becomes much more difficult to handle conflicts of interest, and the system is highly vulnerable to reviewer collusion.