Come to think of it, what's to stop me from making my own free, open-source independent scientific journal right now?

Technically, nothing. Practically, way more than you imagine. First and most important, you almost certainly wouldn't be indexed by large databases. These provide easy metrics for papers and journals that can be easily evauatrd by funding agencies. If you don't have an impact factor, sciencists cannot use a paper published with you to prove to the funders they produced results.

As for other issues you mention later, you usually confirm that the results shown in your published paper was not used in another paper, so exclusivity definitely exists (preprint servers are usually excluded from this).

Good luck finding reviewers in the age of AI. Nobody wants to do it and there are TONS of papers everywhere. Also, you'd need an editor to choose what is even worth sending for review.

Also, I'm not sure issuing DOIs is free, and you must have DOIs.