Under self-published journals I understand a journal brought out by the researchers or research organisatons. I don't see why Germany's or even Europe's universities and research institutions couldn't publish a peer-reviewed and checked journal in collaboration, without a third entity, that can provide the quality of, say, nature.
You mean a university press or a society journal? That model worked extremely well for > 100 years, until in the 1990s the societies sold their journals to Wiley, Springer and Elsevier, and somewhere around that time Springer took a wrong turn. You'd really like to ask why the selloff happened when it did.
In recent years, journals that claim to have a peer review process but which actually offer dubious or no review or quality control have proliferated (some are even published by companies like Elsevier). Having no established reputation doesn't prove that a journal is bad, but having an established reputation is a heuristic shortcut for evaluating whether it is good (at least in the "no one was ever fired for buying IBM" sense). Hiring committees use this heuristic to save time when filtering candidates.
Compare this to a publication in nature. There, by virtue of the name, you know the article is worth more. (Note that in practice, Nature apparently has quite a few sham publications)