I had a flash of insight: they are asking for more materials now because they are tired of weak applications. I have never applied for a job that asked for a research statement, but I always included clear discussion of research in my letter. Now they are separating the components of the letter, and breaking things down to step-by-step instructions … just as we now must, when we assign things to the students.
(My experience is that essays do get much better when you write instructions almost as long as the essay itself is to be — even when teaching at a level where part of being at that level is, or was at one time, no longer needing such instructions.)
Now job candidates need more explicit instructions, or now search committees have organized to improve the quality of job applications. In this process it has become the case that more materials are required than ever before. Things have not become more competitive, but more bureaucratic; and official efforts are being made to ensure that all candidates know how a good application looks.
What do you think of my theory?