Or could tunnel IPv4 over IPv6. We'll call this 4in6.
The mistake you are making is thinking that it is hard to have dual stack. IPv4 will be running in tunnels for a long time, just like IPv6 run in tunnels in early days. There are enough IPv4 addresses for servers for a long time. Eventually, IPv6 will be the norm and nobody will care about IPv4 except for running old hardware and software.
Upgrading just networking software is impossible since client software needs to be upgraded to support longer addresses. In particular, they need to support the generic interfaces that work with multiple protocols.