It is much like a conversation in a chat system, but the etiquette on twitter means your conversation partner usually won't wait for you to finish a string of messages.
It's true that it's easy for people to interject and annoy, and it happens more and more the bigger your celebrity status. However, unlike the interview example, it's also easy to ignore them. Twitter's reply helped a lot for that. Replying to anybody is optional, you don't even have to read their tweets if you don't want to. It's not perfect by any means, I don't think any platform will ever be. But it isn't bad.
It's true that it's easy for people to interject and annoy, and it happens more and more the bigger your celebrity status. However, unlike the interview example, it's also easy to ignore them. Twitter's reply helped a lot for that. Replying to anybody is optional, you don't even have to read their tweets if you don't want to. It's not perfect by any means, I don't think any platform will ever be. But it isn't bad.