This is an easy question to decide once you understand that there's a single thing we're optimizing for on HN, namely intellectual curiosity: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor....
We're not going to ban Twitter because, like it or not, it's the source of some of the most intellectually interesting material that gets posted here. It's also, of course, the source of a lot of gunk. We penalize such sites by default (almost all major media sites are penalized this way on HN), but we don't ban them, because we'd miss out on too many good things if we did. It's more important not to miss good things than it is to ban bad things: https://hn.algolia.com/?dateRange=all&page=0&prefix=false&so...
The paywall question is a different one. See https://news.ycombinator.com/newsfaq.html and https://news.ycombinator.com/item?id=10178989 for how we handle paywalls. I don't think twitter.com is hardwalled, though like a lot of big sites, its behavior seems to vary a lot across different regions. It shouldn't be hard for people to post workarounds in the threads, though.