The average value (bytes/word) only optimizes out the word count step, which can be done fairly efficiently already (shell out to wc, if nothing else). Besides, for our purposes, averages weren't sufficient - it had to be exact.
From that point on, this approach is simply the second one I had detailed with the "aaa...b...cc..." array and it suffers from the same scalability problems. You've got 100 files with 3,000 words each and a 300,000 element array. My method ends up with a 100 element array.
You'll note that I didn't say "quickly", I said "efficiently". I was optimizing not only for execution time, but for memory storage. But yes, for smaller data sets, simply repeating the stored value n times is sufficient.