As usual, one important consideration in this equation makes n-o rational sense at all, but is nevertheless very real: lawsuits.
Someone “out of the blue” is pissed-off at you or at your company and decides to make a big, multi-gazillion dollar stink. The only defense that you have is to show that you had some process, and that you followed it with every employee, and that the employee had some part in it ... as evidenced by something writ in his or her own hand, and signed. It matters much less what the paper actually says, than it does that you can produce it, and show that it bears original handwriting by someone other than the manager. The financial consequences of an adverse judgment, or even of a settlement, can be devastating.