Yes, this is more or less how the non-profit journal https://elifesciences.org https://elifesciences.org (funded by HHMI, Wellcome, Max Planck, and Wallenberg F

Yes, this is more or less how the non-profit journal https://elifesciences.org https://elifesciences.org (funded by HHMI, Wellcome, Max Planck, and Wallenberg Foundation) works. A problematic aspect of non-public peer reviews is waste and political battles. I have witnessed first-hand how big names in a particular field reject articles from incumbents that are perfectly sound just to delay their publication and/or to copy them. A public review introduces some skin in the game and avoids this kind of behavior, as well as rejections or requests to make changes because of reviewer incompetence. It also avoids the opposite thing, blind acceptance of flawed studies.