Are you going to lie and tell it it's 1.1.1.1? Congrats, you've just reinvented NAT. Enjoy your stateful boundary system and all that complexity again.
Are you going to add some extension to IPv4 and try convince everyone to upgrade all their hardware, software and configurations? Then you have the exact same problem IPv6 adoption had, except IPv6 adoption is at like 45% globally and your new scheme is at 0%: https://www.google.com/intl/en/ipv6/statistics.html
If you have some other idea, make sure to check it against the list of IPv6 transition mechanisms before commenting - it probably exists for IPv6, and ultimately all of them have been displaced by dual stacking: https://en.wikipedia.org/wiki/IPv6_transition_mechanism