Yes as I said it’s working as intended. The point of machine id is to id a machine.
Your claim was that Linux was "sending your unique id to any entity you browse" which is misleading at best. machine-id should never be transmitted and if it is, that software should be considered spyware.
A better solution would be to not rely on the various programs to hash the unique id and instead have the host read it, hash it and provide the hash to the program that asked.
That doesn't solve anything, really. There's plenty of ways to fingerprint a machine that doesn't involve the machine-id.