In the end, OS/CPU combinations define ABIs, compiler toolchains (no matter what language) can't do much more then follow (if they want to be able to talk to the operating system at least). E.g. if one day operating systems implement stable Rust-friendly ABIs, then C compilers will have to adapt to those conventions instead.
See https://faultlore.com/blah/c-isnt-a-language/ for more detailed analysis.
Also IIRC it was really only UNIX which had this "whatever our C compiler does" mishmash. On most other operating systems it was the other way around, C compilers had to implement whatever calling convention the OS already had defined before there even was a C compiler for that OS (for instance early Windows version used a PASCAL calling conventions, and others (CP/M, DOS, AmigaOS...) some random rules that were most convenient for handwritten assembly code).
PS: and yeah I know that other article (or rather: incoherent rant). It's basically a lot of barking up the wrong tree.
I'd push back on this a bit. The ABI is "put the arguments on the stack this way and jump to this address". The fact that it's easy to do in C doesn't really make a difference, or make that process "C specific" at all, any other language would need to do the same thing.
If you require those arguments to represent rust objects or be reference-counted in some way, it would impose more restrictions on the caller, not fewer.