The problem with this approach is that smaller universities can't afford to do this.
I think this problem needs to be adressed at funding agency level, with funding agencies requiring that all publication be made available on the agency's website.
+1 to you, but somebody needed to make the first move, and I think most professors at smaller universities would be happy to publish wherever professors at Princeton are publishing.
The cost is that if Podunk University in Podunk, Texas adopts Princeton's policy, Elsevier and Wiley can simply decline to publish anything written by the three Ph.D.s on their faculty. That will make it difficult for Podunk to attract a fourth Ph.D., and even the three it has may choose to give up tenure there in search of someplace they can publish.
However, if a few big universities follow Princeton's lead here, that cost will disappear.
I think this problem needs to be adressed at funding agency level, with funding agencies requiring that all publication be made available on the agency's website.