C – Why Can’t Arrays Be Passed as Function Arguments?

You will probably make it a lot easier on yourself and avoid a lot of user errors if you allow the declaration of variable-length arrays to be delayed until a point where the size is known. Then you don't have to invent a syntax for assigning the array size and you don't have to deal with differences in the order in which arrays are declared and in which they get their size.

If your compiler uses a stack-based allocation scheme for local variables (they are given addresses relative to the stack-frame of their function, like it is done for the 'big' platforms), the variable-length arrays can just be carved out of the stack frame as needed. Only if there are multiple variable-length arrays in a function do you need an additional pointer to indicate where the data of each starts.

If your compiler uses a fixed allocation scheme (all variables, including locals, are given a fixed (absolute) address by the compiler/linker), I would use an 'array stack' for carving the variable-length arrays from. As overhead, you would need a global pointer to indicate where the free space currently starts, a pointer for each variable-length array to indicate where its data is located and, in each function using variable-length arrays, a way to restore the global pointer to the value it had when entering the function.
The user would also need some way to indicate to the compiler/linker how much of a 'array stack' he thinks will be needed. A reasonable default could be to use whatever is left after allocating all fixed-size variables and variable-length array overhead.

I think this scheme uses the least amount of overhead, both space and time-wise. The scheme you came up with is essentially a malloc implementation.

How would your proposed extension handle the situation where a multi-dimensional array isn't allocated statically? Having the extension be limited to cases where the allocation is static would make its behavior inconsistent with other array handling, but if the extension isn't limited to static array allocations then passing a double[5000][5000] to function which is expecting a double** would require the compiler to generate and fully populate a (double*)[5000], even if the function wouldn't use most of (or even any of) its elements each time the function was called.

A more useful extension might be to add types like double[][] and double[][][] as types in the language, and have each such type with N dimensions be stored as a double* along with N-1 values of type type size_t. It would be necessary to have separate methods for jagged and linear arrays, but it would not be necessary to have different methods for each size of linear array.