You are wrong, and I say that as someone who was employed by someone who (likely) invaded and still invades your privacy through a firewall and IPv6.
Modern firewalls do nothing for privacy. IPv6 eliminates your ability to maintain your privacy.
Security is a different matter, and NAT doesn't add much there (although it is another layer). But the comment you quoted was specifically about privacy.
Even though you're right, privacy is quite irrelevant in this case anyway. If no one can walk through the door, your personal space cannot be violated. If you want to hide your IP use VPN. You essentially should not rely on things out of your control, such as CGNAT. But yeah, I agree, I should have mentioned security, only.
My threat model excludes state actors and my ISP actively collaborating with those who try to profile me. Thus, CGNAT - which I already get, is comparable to VPN (better in some respects, worse in others).
This comment. Every single time. No it doesn't. NAT doesn't add privacy. NAT doesn't add security. Use firewall with IPv6. This is it.