Over and over I emphasize that Twitter is not a public utility. If you're an organization that has to get your micromessage out there, you're better off hosting your own services.
Are you just trying to post/read feeds as an individual? If that is the case the open alternative does not provide you a benefit, and you will probably find it less convenient.
On the other hand, what if you have many users under one org? How about you're just a member of a division of another org, and they have many division and subdivisions. And they really want be sure that your message gets out there, without relying on a third party. The public relies on those messages, for example a fire department posting about wildfires. Those are the use cases that will probably see benefits.
If you have the infrastructure to handle a setup like that, you should already have an internal email server.
EDIT: After your edit, I think I've found where the disconnect is from my perspective. The problem with this method is that discovery(arguably the most important part of what Twitter provides) is still reliant on a third party's index.
From a user's perspective, Twitter provides 3 key services from one URL:
1. A unified feed for everyone you follow(This proposal also does this).
2. An easy way to post/host content(This proposal does not deal with this).
3. An easy way to discover new people to follow(This proposal also does not deal with this).
Out of those three, I would argue that the second and third are the most important. The problem isn't getting the message out to people that are already subscribed with Twitter, email, or a hosted website. The problem is discovery, and giving people an easy way to actually find the information that they're looking for.
The only way to handle discovery on this way is to have some hosted, third party method of searching through the users to find the ones you want to follow.
People won't be using this new decentralized service. They'll be using Twitter. I guess you can feed into Twitter, but the last mile is still Twitter.
Twitter will not make or break most organizations. If it were to disappear tomorrow most any organization will have plenty of time to look for alternatives. In the meantime Twitter wins. Always. By a mile.
I'm not really sure it matters where the users are. Ideally in a well designed system/protocol, it shouldn't matter. Email solved that problem 30 years ago.
This is something no single organization can solve. It's impossible. And email is about the absolute worst example. No, it absolutely didn't solve the problem. First the users had to come. Before that it was worthless.
I think many here are delusional about how this works.