> For example, in IPv4 each host has one local net address, and the gateway uses NAT to let it speak with the Internet. Simple and clean.

No, that’s not the IPv4 design. That’s an incredibly ugly hack to cope with IPv4 address shortage. It was never meant to work this way. IPv6 fixes this to again work like the original, simpler design, without ”local” addresses or NAT.

> In IPv6 each host has multiple global addresses.

Not necessarily. You can quite easily give each host one, and only one, static IPv6 address, just like with old-style IPv4.