I suspect by "incredibly conservative" you mean "backwards compatible", which... no. You can't make an addressing extension backwards compatible with hardware that doesn't read all of the address. Of course, we did that anyway with CGNAT, and predictably it causes huge problems with end-to-end connectivity, which is the whole point of IPv6. You're probably thinking more along the lines of an explicit "extension addressing header" for v4. Problem is, that'd mean a more awkward version of IPv6's /64 address split[0], combined with all sorts of annoying connectivity problems. The same corporate middleboxes that refuse to upgrade to IPv6 also choke on anything that isn't TCP traffic to ports 80 and 443. So you'd need Happy Eyeballs style racing between CGNAT IPv4 and "extended IPv4".
Also, that would just be a worse version of 6in4. Because they also thought of just tunneling IPv6 traffic in IPv4 links. I don't think you understand how incredibly conservative IPv6 actually is.
The problem with "incredibly conservative" IP extensions is that nothing beats the conservatism of doing literally nothing. IT infrastructure is never ripped out and replaced unless there is a business case for doing so. The current problem with IPv6 adoption is that nobody has yet said "let's stop processing IPv4 traffic", they've only said "let's get more dual-stack hosts online", which is a process that only asymptotes to 100% IPv6, and never reaches it.
IPv4 was not the first version of the Internet protocol. That honor goes to Network Control Protocol (NCP). The reason why we don't have an asymptotic long tail of Internet hosts still demanding NCP connectivity is because this was back when "having a connection to the Internet" meant "having a connection to ARPANET". The US military could just refuse to process NCP packets and actively did this to force people onto IPv4. Now imagine if someone big like Google said "we're going to stop accepting IPv4 connections" - people would jump onto v6 immediately.
[0] Let's say we add a 32-bit extension header onto IPv4