As I posted this idea on a few forums I have had various responses.
With adaptation there is a possible solution. We do not just send byte length and checksum, we also send clues.
We send the file type to be produced, the byte length, the checksum, the first and last few characters(?), a 1 or 0 to show if 1 or 0 is more common in the file, and well anything that would help the generating algorithm on the local computer to attempt more suitable guesses.
Like if I had a 6 sided dice in my hand I do not ask you (the algorithm) to bother with colours, numbers above 6, letters of the alphabet, animals, vegetables or politicians. I give you a much better chance of getting the answer.
So in the case of a file I say. It is a .png, 4370120bytes, checksum blablabla, starting with a 1 and mainly 1's.
..obviously I don't really know what I'm talking about
but I feel the idea has legs if people add such ideas to the basic premise.