If an address is not public how can you start an connection from it, or end a connection at it? A web server needs a public address if you want to have people reach it. And you, at some point, also have to have a public address if you want to connect to pubic services: either on your end-host, at your CPE/router's WAN interface, or on an interface of your ISP's CG-NAT box.

But having a public address on your end-host also allows for much more functionality than if you were stuck behind CPE-NAT or CG-NAT. Now, you don't have to use this functionality—just like how I didn't when my printer gets an publicly addressable (but not publicly reachable) IPv6 address—but it opens up various possibilities.