I think “please” could be construed as shorthand for “if you please”, as in “Sign this form and mail it back to me if you please.” It gives the person receiving the request the illusion of some sort of option to decline, which perhaps makes it more polite.

At work, I regularly issue requests to people who do not report to me and whose relationship to me in the management hierarchy is unclear (contractors who work for a firm for whom I also do contract work). I regularly issue “please” commands hoping that they will comply, and hoping that I don’t sound to presumptive in issuing the command.

When issued between distinctly unequal parties (i.e., my bank to me, or me to my daughter), it may have become a form of wrote courtesy which has lost all sincere meaning.

P.S. “To complete this form, please complete the word verification below.” [emphasis added] Rich, if you have a minute, can you “please” put me on the capcha-free list? Come to think of it, I think I’m going to make scare quotes a regular part of my “pleases”.