What is the rationale for fread/fwrite taking size and count as arguments?

It's based on how fread is implemented.

The Single UNIX Specification says

For each object, size calls shall be made to the fgetc() function and the results stored, in the order read, in an array of unsigned char exactly overlaying the object.

fgetc also has this note:

Since fgetc() operates on bytes, reading a character consisting of multiple bytes (or "a multi-byte character") may require multiple calls to fgetc().

Of course, this predates fancy variable-byte character encodings like UTF-8.

The SUS notes that this is actually taken from the ISO C documents.

The difference in fread(buf, 1000, 1, stream) and fread(buf, 1, 1000, stream) is, that in the first case you get only one chunk of 1000 bytes or nothing, if the file is smaller and in the second case you get everything in the file less than and up to 1000 bytes.

This is pure speculations, however back in the days(Some are still around) many filesystems were not simple byte streams on a hard drive.

Many file systems were record based, thus to satisfy such filesystems in an efficient manner, you'll have to specify the number of items ("records"), allowing fwrite/fread to operate on the storage as records, not just byte streams.