Yes, you can bypass all of this and put your non-reviewed pdfs on your personal website. No one will care, in part because no one will even know and if they do, they have to do the hard work of review in order to decide whether a paper is worth trusting. But how will anyone find out?
As an author, I've made a point never to publish in a paper not backed by a non-profit scientific society with a decent open-access policy, after doing so in the past. I also put all of my pdfs on my website including appropriate white papers that are working drafts, making it clear to others that they haven't been accepted through peer review.
As a reader, however, I keep up with the literature (aside from targeted Google Scholar searches) through Table of Contents emails from a few journals--mostly non-profit society journals but a few others including Nature. The editorial curation aspects which limit the number of accepted papers per issue make this possible. I'm not going to drink from the firehose of shit that is produced each month, especially before peer-review. Yeah, it sucks when your paper is accepted by reviewers but gets nixed by the editors because it's not cool enough, but... you know, get back to the bench and make it cooler if you want people to care. Welcome to the 21st century and attention scarcity.
You can change the name 'Nature' to whatever open-access journal you'd like, but the power behind it is that it's a sign that Important People have decided your paper is one of the 10 most impactful papers in your field that year. That's why people care.
Nature is just a bunch of noted academics that come together and do peer-review (for free btw)... is that enough value creation to charge exorbitant amounts to universities and block content to the public that is funded by government grants?
If academics could build a peer-review board themselves (hint: now they can... thanks internet!) ... then everyone would have free access to science.
Universities in less rich countries would be on a more level playing field, if these massive subscriptions were not table stakes.
Journals do provide some value. Editing, printing, and herding academics through the camera-ready process all require non-trivial effort.
I would have absolutely no problem with a handful of universities/non-profits/even for-profits devoting some staff to the curation/archival process. And also no problem with those organizations charging others modest fees to fund that work.
The problem with journals is that they capture a lot more value than they provide, that value is not distributed back to the people doing the actual work, and the prestige signal/branding provides a strong moat.
I REALLY think this is an important point. If we continue to behave like all of this stuff is trivial and obvious to replicate, then we'll be forever stuck with predatory journals like Nature.