I mean something a bit different. I mean using PE binaries to store Linux programs, no Wine loader.

Of course, this is a little silly. It would require massively rethinking many aspects of the Linux userland, like the libc design. However, I honestly would be OK with this future. I don't really care that much for ELF or its consequences, and there are PE32+ binaries all over the place anyways, so may as well embrace it. Linux itself is often a PE32+ binary, for the sake of EFI stub/UKI.

(You could also implement this with binfmt_misc, sure, but then you'd still need at least an ELF binary for the init binary and/or a loader.)

(edit: But like I said, it's a little silly. It breaks all kinds of shit. Symbol interposition stops working. The libdl API breaks. You can't LD_PRELOAD. The libpthread trick to make errno a thread local breaks. Etc, etc.)