Any solution that requires updating clients, servers, and networking equipment to support the protocol and/or adjust the network address scheme of the environment will require the exact same steps doing an IPV4 to IPV6 migration would require.
Whatever you do to get more addresses, it will look similar in the end, but the steps could've been very different.
How would a router know what to do with it without updating its software?
At the end of the day, you are talking about using a different than IPV4 address scheme and using a different protocol than IPV4. Everything in the stack will need to be updated. Every hop on the route, every single piece of software that will interact with the network address. Backwards compatibility still requires everything but the older device to be updated.
Then once there's sufficient v6 adoption, you can disable v4 entirely and start using /40, /48, etc..
My confusion in the claims that we could do it differently is how the protocol could be updated without actually doing the work of updating everything on the network and adding the new address scheme.
But same addr is the problem we are trying to solve in the first place. Using your IP-new proposal (let's call it IPv5): If every IPv5 addr is just a padded version of the same IPv4 addr, then once IPv4 addresses are exhausted the IPv4-mapped-into-IPv5 addresses are also exhausted.
At that point you need to start handing out IPv5 addresses to hosts without an IPv4 address. And then, how does a IPv5-only host talk to a IPv4-only legacy host? That's the fundamental issue!
The same addr thing only buys you time until the address exhaustion becomes real.
Ipv5 as you call it: Phase 1 is getting routers/hosts to understand v5 headers, while users enable v5 and change nothing else. Phase 2 is the transition where people keep using padded addrs while things* are updated in-place to just support longer ones, which doesn't affect users**. Once that's done, we get to use the full space, which some users may ignore and some may use. For better and worse, the existing /32 blocks would still be around initially. Maybe this would appeal to previous ipv4 holders better; they still own the same % of the pie. Maybe 8.8.8.8 would stay forever.
What makes me kinda sure would've worked? Right now, the world has mostly already completed the equivalent of phases 1 and 2 for ipv6. There might even be a way to reuse the ipv6 protocol as-is for ipv5.
* DNS, NAT, DHCP, ARP, routers, VPSes, OSes...
** "User" includes corp network admins, cloud/datacenter operators, ISPs, and simple home customers.