If I understood it correctly, unfortunately, I think your question in some ways answers itself, in the sense that the rich become richer and the powerful remain more powerful.
An impact factor, just like anything else or any of the metrics that are used, can be used to essentially cement and consolidate funding and, I could even argue, power—but that is actually another reason why these are such problematic metrics.
Again, researchers at those institutions tend to be cited more often anyway, and then they can just double down on that, so they have no particular incentive. I would credit those institutions that are wealthy in terms of funding and that have signed the declaration or taken other measures, because I think it signals a real intellectual honesty and a willingness to change that might benefit everyone instead of just continuing the Matthew effect.