Even today, when you look at the core routines of for instance X windows C is still used in exactly that way, you don't have to but you definitely can and even though C compilers have advances tremendously the fact that there is a direct 1:1 correspondence between input and output is exactly why C is used in those situations.
C supports multiple stacks if you tweak setjmp and longjmp just right, and using co-operative multi-threading is possible without any OS support. Not very useful if you really have to do two things at the same time but a lot nicer than interleaving a bunch of code.
And an optimizing compiler is still a transformation of the input according to a given ruleset, you could not get the same level of optimization by just processing the output of the code generation stage of the compiler because you would lose a bunch of higher level information that is invaluable when optimizing the code but you could see it as just another stage in 'transforming' from one language to another without losing any functional bits along the way.
There simply isn't a 1:1 correspondence between C and its machine code; not in size, and not in functionality.
Any half-decent compiler is going to perform a non-trivial transformation of a big switch statement to make it efficient. The expected performance semantics of a switch (something better than O(n) in the number of cases) rules out simplistic iterated jumps in big cases. The programmer expects O(1), or at worst, O(log n).
But more importantly, CPUs generally have many more capabilities than are exposed by C, and this is where the "1:1 correspondence" really falls down. Assemblers generally have disassemblers that you can transparently round-trip through. That's a little harder in C.
Perhaps you meant a injective relation, rather than bijective? But that's a long way short of an assembler.
"But more importantly, CPUs generally have many more capabilities than are exposed by C."
Hear, hear! Moreover, that has always been the case. As an example, try implementing multiple-word addition in C. On most architectures, you will learn that not having access to a carry bit makes that harder than it could be.
Yes, you're right, the switch statement is a good example of how modern compilers fudge the boundary.
But the main point is that the difference between the generated code and the stuff you write is relatively small, when looking at the assembly that a C compiler generates I have relatively little trouble following the relationship between the two, and I can make reasonable predictions about what will pop out on the other end.
And of course processors are 'richer' than what most C compilers will use, especially when it comes to special instructions that have no equivalent in the C language.
I've worked on a 'decompiler' for the Mark Williams C compiler (yes, that's pretty long ago), and at the time the above still held true, today the boundaries are definitely fuzzier, mostly due to the increased smarts of compiler writers for the optimization stage.
Gcc is clever enough to optimize whole branches of code out of existence if you set it to be aggressive enough and the code was written naively, that's one way of dramatically losing that 1:1 correspondence.
C supports multiple stacks if you tweak setjmp and longjmp just right, and using co-operative multi-threading is possible without any OS support. Not very useful if you really have to do two things at the same time but a lot nicer than interleaving a bunch of code.
And an optimizing compiler is still a transformation of the input according to a given ruleset, you could not get the same level of optimization by just processing the output of the code generation stage of the compiler because you would lose a bunch of higher level information that is invaluable when optimizing the code but you could see it as just another stage in 'transforming' from one language to another without losing any functional bits along the way.