Just to address the implication (prevalent in many of the sibling comments as well) that I and everyone else who talks about this are idiots incapable of grasping that 128 is larger than 32:
If 32 bit IPv4 addresses are valid IPv6 addresses without fiddly NAT64/DNS64 shenanigans, then (it seems to me) IPv4-only clients could blithely continue to interact with the IPv4-accessible internet via IPv6-only servers, routers, etc. indefinitely. They can putter along accessing only a subset of available resources forever and everyone can passive-aggressively roll their eyes at them and close support tickets saying "upgrade to IPv6 if you want to see the rest of the internet, it just works."
That's what I mean by backwards compatible. Everyone who says "it can't be done, it has to be this way" is asserting that there's no better alternative to NAT64/DNS64 and running two entirely separate networking stacks in parallel. I don't buy that there was no simpler way to accomplish packing 32 bits into a space that can contain 128 bits. And if "supporting IPv6" simply meant "upgrading your networking software to the latest version, which transparently handles both IPv4 and IPv6 traffic for you" then networking and server teams have no excuse to avoid deploying IPv6 support for 26 years.
I recognize that 128 bit addresses will be truncated and packets misdirected or rejected if handled by a 32 bit networking stack. I recognize that clients upgrading too early will fail and need to fall back. But making it unnecessarily difficult for servers and routers to handle IPv4 traffic in an IPv6-only context led us to where we are today.
To illustrate my point: ascii text works just fine, with no translation layer required, when parsed and transmitted as UTF-8.