No, there are no exclusivity agreements. It's a jungle, especially for prestige journals. A lot of scientists just push hard for prestigious journals, especially pre-tenure as prestigious journals supposedly impress tenure review panels. While I personally have my doubts that prestigious journals impress anyone, those who don't push for prestigious journals are often viewed as unable to publish high quality work, so at a minimum, most scientists submit to the most prestigious journal they think will accept them (i.e. mid-tier journals).

When they don't look for prestige, they're usually looking at social factors. Do my peers publish here? Is this associated with one of my societies? This is why some scientists associate more strongly with society journals, but it's certainly not exclusive. While there are free journals out there that will publish whatever you send them, they're mostly filled with trash that respectable scientists don't want to be associated with. A new cheap or free journal comes with that stigma attached -- whether they want it or not.

The problem with peer review is that there are often only a hand full of people in the whole world who have what's required to look at things carefully and ask the relevant questions. You need the technical background and niche familiarity - including having kept up the developments in the niche. Usually the journal editor only knows the field (the broad category of work), so journals ask the author to recommend reviewers. Fraudsters can pretty easily shuffle about reviewers and authors while sticking new names on papers as collaborators, citing previous fraud to boost citations, and publishing stuff that looks broadly like science -- even adding (meaningless, easily obtained) data. It's hard to catch because you don't really know any of the people and can't really tell if the science is uninteresting or part of a ring of fraud.

That's why I think it's better to be established in your community before you push too into strange or radical ideas. You don't have to chase prestige, but do enough to be a known quantity that does good work.