Why does `free` in C not take the number of bytes to be freed?

Question

Just to be clear: I do know that malloc and free are implemented in the C library, which usually allocates chunks of memory from the OS and does it

Answer 1

I don't see how an allocator would work that does not track the size of its allocations. If it didn't do this, how would it know which memory is available to satisfy a future malloc request? It has to at least store some sort of data structure containing addresses and lengths, to indicate where the available memory blocks are. (And of course, storing a list of free spaces is equivalent to storing a list of allocated spaces).