Only CG-NAT provides any semblance of "privacy" from the perspective of the outside world, but is a hideous technology that shouldn't exist.
Normal NAT as seen with home internet routers provides zero privacy, because you still have a predictable public IP.
People also think that IPv4+NAT provides security, but IPv4 is such a tiny address space that all public IPs are scanned daily by various malicious bots. Meanwhile IPv6 is so enormous that unless you register your address in some public way, you're completely invisible to port-scanning bots by default!
I have a friend who works in the networking division of a telco in my country, their team had to spend significant time and effort educating a PM who was dead-to-rights convinced that IPv6 was “less secure” and seemed to think that IPv6 didn’t have subnets and that NAT’s were the same as firewalls and refused to be convinced otherwise.
People like that make any forward progress extremely difficult.
It's such a perfect example of erroneous thinking that it should be included in psychology textbooks.
"A always comes with B, hence A is required to provide B" is obviously, trivially wrong, but a truly incredible number of people will dig their heels in and refuse to admit that "B can be provided in other ways".
In this case where things went wrong was that: "Before A the availability B was rare, and A requires B, and hence B become commonplace only because of A."
You can see how the association can be accidentally upgraded to an "if and only if" instead of merely "if".
Normal NAT as seen with home internet routers provides zero privacy, because you still have a predictable public IP.
People also think that IPv4+NAT provides security, but IPv4 is such a tiny address space that all public IPs are scanned daily by various malicious bots. Meanwhile IPv6 is so enormous that unless you register your address in some public way, you're completely invisible to port-scanning bots by default!