Will anybody actually read your research and teaching statements?
I am the chair of the faculty recruiting committee in a Very Good Department at a Big Research University.  I read research and teaching statements.

I need to know that you have a compelling agenda for your future research; your letters won't talk about that at all.  I need to know that you can describe and motivate your research agenda well enough to attract external research funding.  I need to know that you know why (not just "that") your work is interesting, visible, important, and likely to have high impact.  I need to know that you communicate clearly enough to be a good teacher, and that you care enough about teaching to formulate a coherent teaching philosophy.  I need to know that your research, teaching, and career goals—as you describe them—match those of my department.  I need to know that you are taking the recruiting process seriously.

In the long run, your publications (which I also read) and your recommendation letters are probably more important.  But saying that your statements have no importance is a dangerous exaggeration.

Also, I don't eat in the cafeteria.