Honestly, I'd say it's much worse than using your phone number or SSN. Sure, an SSN makes it easier to tie an identity to a person, but it doesn't instill a false sense of anonymity in the user.

Again, for the practical example, people bought and sold bitcoins with the broad assumption that it was anonymous. It's a widely understood falsehood, yet new people almost universally believed it was anonymous and safe from law enforcement/the tax man.

Pretending that a random yet static ID adds any level of anonymity is simply dangerous. At best, it keeps honest people honest; like locking your door but not the bay window next to it.