The "difficult" thing about AVX is that Intel has patented any kind of execution of AVX instruction, including them being emulated or translated into other instruction sets. I am not kidding, it's written there in their patent. I have no idea how the patent office let this through, but we have what we have. Unless you want to risk a very expensive lawsuit, supporting AVX is a no-go.
Why wouldn't it? Sure, Apple would need to spill a single AVX instruction into multiple NEON instructions, but they have enough SIMD units to compensate for this. Here is a real-world tests showing that Apple's 128-bit NEON is equivalent to Intel's 256-bit AVX2 despite the Apple CPU running at much lower speed: https://lemire.me/blog/2020/12/13/arm-macbook-vs-intel-macbook-a-simd-benchmark/
And besides, supporting AVX2 in Rosetta would allow more x86 applications to run. No, the reason why it's not supported is not a technical one. I think it's fairly likely that it's the patent issue.
Do you know the patent number?