now regret to the point that you're willing to rewrite history
And this is bad how? Its your history. If you post something and a week later you decide it probably shouldn't be public knowledge, who really cares if you take it down? Its not like you (for most values of "you" at least) are the sole historian of an important event or other politically-charged information.
Hell.. its your own page.. does it matter if you just write complete BS in the first place?
You're acting like a social network is a web site. It's not, it's a fabric. If you want to be able to do this type of editing, fine, put up a web page, but don't try to pretend that you posting something that makes you look like an asshole, and then me commenting on it, calling you out for being an asshole, and then you changing the original posting so that it looks like I'm the asshole for engaging in an ad hominim attack, is somehow OK.
What the OP has suggested is more or less the old Usenet, but with a single point of failure for me being able to access the shared history of the gestalt of people who were engaged in the conversation or conversations that resulted in that gestalt in the first place. If I'm connected to you and Bob and Tom and etc., we're not just connected through our freedom of association choices, we're also connected by our shared context and history.
I'm also not sure I'd be comfortable with some types of content showing up in "my feed", particularly content that happens to be illegal in my jurisdiction. I certainly don't want ... able to post Nazi propaganda into Germany, ...
So don't be friends with people who would do that. And if you don't know about their leanings before they post that shit, you can just de-friend them and delete their rant (see above.)
See above; I can't just erase our shared context from my memory, if I decide Bob is a Nazi after the fact. One of the problems with Facebook is one of things which make it useful: the extended shared social network, where I not only see what you write in a conversation, but because Bob knows you, and you know me, I get to see Bob being an ass because of his association with you. Am I just supposed to "de-friend" everyone? How do I know that I'm seeing Bob because of you, and not Tom? Maybe I'm seeing him because of both you *and* Tom?
I don't have much to say on your third point as it would be wholly dependent on actual implementation as to whether this theoretical distributed service provides "weak" or "strong" links (whatever the hell that means.)
Also keep in mind that Facebook and Twitter are completely different services with completely different purposes. They may have been glommed together under the "social media" category but that's like saying cats and dogs are the same thing because they both fall into the "common pet" category. They have similarities to be sure, but they have far more in the way of differences.
Twitter's links are "strong" because if you "follow" them, you see every little thing they post. Facebook's links are "weak", because if you "follow" someone, you don't necessarily see every little thing they post.
The reason that offline social networks work is because you have transient freedom of association. You have less of that with Facebook, and drastically less of that with Twitter. That's why Twitter is basically a troll-sewer, and Facebook is less of one.
Another reason for the "troll-sewer" effect is that there is no longer term consequence, if you can delete your posts after the fact. By allowing the rewrite of history (discussed earlier), you remove the need for the social lubricants of politeness, civility, and (possibly pretend) rationality, which are required in real-world interactions. Because of that you end up with large amounts of vitriol over things which would have blown over, or which people would have just avoided commenting on in the first place, in order to try to keep the peace with someone they disagreed with over some issue they brought up.
If anything eventually dooms social networking, it's going to be the "Twitter effect", where people's mood swings are driven harmonic oscillators; at least Facebook is a damped, driven harmonic oscillator, and as a worst case scenario, by reducing what you see of your friends posts, or of reactive posts that tend to blow up into large threads, they have the ability to damp it further by pushing in the control rods.
A social network of the type that the OP suggested combines the worst effects of Twitter, with the worst effects of removing accountability. IT would be a highly chaotic and unstable system. This is perhaps what the OP wanted in the first place, but it's not a place most of us would choose to participate in, or participate in creating so that he could feel good about having one.