Well, IPswen can do this trick in a relatively simple way, and easily "squeezes" the whole IPv4 address space into its shortest length "level 0" base address space. The secret is simple: yes, variable length encoding. You may refer to the above reply for details.
That article is from 2002, and arguments like that have been shot down repeatedly since then.
It's a bit long-winded, but the essential argument is that IPv6 introduces a breaking change by definition -- more addresses than IPv4 supported. That's the point. Either you abandon this benefit, or break direct compatibility with IPv4. It's possible to proxy, or tunnel over IPv4, and there a few corner cases that "might" work, but the general case simply cannot.
E.g.: If you support IPv6 -> IPv4 translation, then this must occur either in the host, or on the first-hop router, which must also become highly stateful so that it can return the traffic to the correct IPv6 host. This essentially means that you have IPv4 + IPv6 coexisting side-by-side either on the host or its immediate upstream. This is literally dual-stack! That's why this is the solution that has been adopted by the industry. It works. Everything else doesn't.
Whatever else you're about to suggest has a counter-example where it just won't work. There aren't two toy hosts on the Internet, there are billions. There aren't a couple of routers under your control, there are hundreds of millions, most of which are replaced infrequently.
Solutions for migrations must cater for every bizarre scenario, not just simplified ones required to make that solution work.
Solutions must not require highly stateful routers, because at telco scale, that just doesn't work.
Etc...
These ideas have been discussed at length by experts in the field, and have been shot down decades ago.
Yet the issues they brought up still persist today and are a sobering indictment why IPv6 (as IPng) fail to reach the objective it originally set forth.
Also, the link I posted doesn't involve highly stateful routers. It's talking about getting IPv4 clients that is IPv6 aware being able to IPv6 hosts without the involvement of an IPv6 gateway aside from Anycast gateway that could be outside of the balliwick of the client. Something tells me you don't understand what was being proposed.