True, but at least it prevents them from linking accounts. It is equivalent to no profile picture, which you might not want to keep up appearances.
You may be surprised to learn that your face is your least identifying trait online. You network of friends/followers/likes identifies you far more readily—even if you use a random username.[1]
Managing your privacy is a lot like CPU side channel attacks. It forces you to re-evaluate your fundamental assumptions about what information can be exploited.
Its presumed lack of falsifiability has been one of its drawbacks and has been the source of some of the controversy around it.
Finding a potential test that could be conducted with telescopes instead of high energy particle accelerators would be a big moment in modern physics.