NAT is a cruicial privacy and security feature.
"No need to use NAT" is, of course, a horrible anti-feature, not a benefit of IPv6. (And, of course, in the real world the vast majority of IPv6 is rolled out with NAT anyways.)
As for privacy - you can fingerprint individual devices pretty trivially, and with privacy extensions for SLAAC you can only tell what /64 network it's coming from, which is no more information than IPv4 (unless you're behind CGNAT, but frankly being behind a 4-to-4 CGNAT shouldn't count as internet access because you literally can't get incoming connections.)
I don't have any hard stats, but NAT seems to be very rare in v6 deployments. You don't really hear of ISPs using it. I'm certain you could find some if you looked hard enough, but mostly it's not a thing.
IPv6 security is like IPv4 security: Firewalls
For privacy IPv6 uses Security Extensions, which shuffles your ipv6 ip.
The world can mostly function without NAT. It's mainly only used to work around address shortages, which aren't an issue on v6, so there's simply no reason to use it most of the time. It can be a useful tool in your toolbox, but it's one that you only need to use very rarely.
Here's a benefit from v6: 40% faster connection setup†. Measurable benefits show that there are benefits. "No need to use NAT" is of course another obvious benefit of v6.
†: https://www.zdnet.com/article/apple-tells-app-devs-to-use-ip....