It’s very noisy. For anons, it’s literally the only “button” on posts, so there was an extra line under every post with a single button dangling there.
At Stack Exchange we found that users shared URLs from the address bar way more than any particular share button. In fact, explicit sharing buttons were removed due to lack of use:
analytics show us that a great many of posts are shared, but nobody uses the share buttons to do so. Note that we always show the question share buttons to everyone, always, and they also get garbage usage. Looks like people would much rather copy/paste links than use those buttons, no matter what the display rules are. This change is testing that hypothesis. link
(tests bore out the hypothesis, by the way)
That’s a good point, though – we should make the share button on the topic visible to anonymous users, since it’s not repeated on every post, and offers another vector.