I actually disagree: that's the road taken. NAT is practically this. When you're behind a NAT, you're effectively using a 64-bit address space. Two more layers of NAT, and you can have 128-bit address space. "The first part" of the address is a globally routable IPv4 address, and the rest is kept by the routers on the path tracking NAT connection states.

And NAT needed zero software changes. That's why it's won. It brought the benefits of whatever extension protocol with existing mechanisms of IPv4.

IPv6 isn't an alternative to IPv4, it's an alternative to all IPv4xes.