I disagree on one point; namely I think most of the suck surrounding Twitter has to do with a few UI decisions that could be tweaked at little cost. Not broad philosophical notions (dare I say: bloviating wankery from @jack) of what "healthy conversation" is. This is a topic that's indescribably far out of Twitter's wheelhouse.

1. Notification throttling

The experience when you receive a bunch of replies is terrible. Even if those replies are good (but especially when they're negative), you're still dealing with your phone filling your notification screen. It leads easily to feeling dogpiled, especially if the character of the replies isn't positive. They quickly become too many to read and deal with.

Notifications should stop after around 5 to 10 replies to the same tweet, user-configurable.

2. Conversation muting

It's all too easy to wind up in a long conversation you don't want to be in anymore. Since tweet chains use direct @uernames, the only way to get out of the conversation is to block the offenders (which is a nuke where a knife is needed), or ask nicely for people to drop your username and hope they comply.

There should be a way to opt out of further notifications in the same chain of tweets.

These two things alone would do wonders to improve the user experience.