You could, but does your device actually do so? Are you confident that 100% of the devices you own use privacy addresses and do not leak non-privacy addresses?

The nice thing about IPv4 NAT is that you plug a single gadget in to your ISP's connection (cable modem, ONT, whatever), you connect your devices to that gadget, and it works out of the box and has all the security properties you'd expect, even if you're a person who hasn't ever thought about security properties and doesn't know what IP is and is still running Windows XP because your word processor still works fine. It might be unclean, but the benefits of this model are immense.