In my view that is probably one of the worst ideas that i have heard. That those who are supposed to be a beacon of integrity are now outsourcing the integrity control to the private sector. That´s what happens when some intelligent scientists make decisions guided solely by the (German) efficiency criteria.
Not to mention all the financial consequences that will come from such an absurd idea.
I bet that from now on the papers that were not previously screened by the notorious private integrity inspectors (that poor countries cannot afford) will now have fewer chances of being accepted by major journals. Just because publishers are experts in reducing costs at the expenses of universities that already provide pro bono peer review services. No doubt the scientists who came out we that brainless (but highly profitable) idea are publisher's best friends. Let´s not forget that private integrity inspectors can do nothing to solve or even detecte the low integrity problem mentioned in here https://pacheco-torgal.blogspot.com/2019/10/omnipotent-omniscient-omnipresent-and.html
Wouldn´t it be simpler for academia to change the reward system instead which is the root of all (low integrity) evil as per Edwards and Roy paper?
Edwards, M.A. and Roy, S., 2017. Academic research in the 21st century: Maintaining scientific integrity in a climate of perverse incentives and hypercompetition. Environmental Engineering Science, 34(1), pp.51-61.
On the current reward perversion and on the publication deluge (AKA neophilia disease) see also: