A public DNS with unique canonical names would be nice, but we don't have one of those. The DNS we actually have is inconsistent for several reasons: replication lag, ownership disputes, legal and political disputes (governments disagree what content is ok), VPNs with custom entries, firewalls, host files, etc, etc.
URIs are incredibly important and deserve a more solid foundation to build upon. To make them truly unique, we should use some form of GUIDs. Pet names are a usability layer on top of GUIDs for us humans , but we should communicate the GUID instead of or alongside the pet name.