Instead of asking "How do we become "non-unique""?
We could ask "How do we send less data to the parties who want to do tracking?"
For example,
User A sends 2-3 HTTP headers, the bare minimum, e.g., Host, Connection, maybe User-Agent or Cookie in some instances if required. User A has disabled Javascript unless she needs it.
User B sends a potentially unlimited number of HTTP headers (User B does not care to control the headers she sends, she just leaves that to the applications). User B leaves Javascript enabled regardless of whether it is needed.
Each user may be "unique", with sufficient effort from the party doing tracking, but there's an argument that User A is less interesting to the tracking parties than User B. Both users have footprints, both can be tracked, but one is sending much more data to the trackers than the other. She's leaving more detailed tracks, so to speak. User A is leaving a more generic footprint.
There is also an argument that finding "uniqueness" among a large group of "User B's" would be easier than amongst a large group of "User A's". If we were trying to achieve the impossible goal of "non-uniqueness" it would arguably be easier to try to have all users appear to be identical to User A than trying to get all users to match User B what with all the additional potential variables User B presents thanks to uncontrolled HTTP headers and Javascript's access to her computer's resources (and all the potential issues and "options" that raises).