Was this an oversight ?
No, this was intentional.
We ran some analytics and found that very, very few people made use of those share buttons. And while I'm glad you found them useful, considerably more people actively resented them.
Since they weren't really working, weren't really popular, and were cluttering up every question we removed them.
May we use Twitter independently ?
Our data does show that a lot of our users like and use Twitter (they just don't like or use the buttons).
Copying a url from the link popup into Twitter (or Facebook or G+) is equivalent to using the old share buttons.
The Announcer and Publicist badges are still awarded when you share this way.