There is probably little if anything to add.
Bureaucracy of that kind is common. Particularly with bosses that are not in control, or in organizations that are not of the business kind.
The one or two organizations I used to work in and that demanded employees to sing in and sign out, were quite ineffective and that was the only kind of control employed as bosses there had not much clue as how to control the real work effects, so they had to resort to "time control". Though I'm not telling it's happening with all such organizations, just my experience.
What measures will be taken to protect the binder since it will be used by one staff member to say how much sick and vacation time remains?
Not sure if that works that way in US, where I'm from we always get an official signed paper for vacation (signed by boss) or sick leave (signed by doc), so that if the payroll staff or employee responsible for tracking it, will make an error, I have the papers to prove them wrong.
Generally, IMHO the timesheets are not that big thing on their own, unless they are a vanguard of further bureaucratic provisions to come from the side of your boss.
Just on a sidenote, my father used to work in school environment, and he changed soon, claiming that the "management" there just thinks completely differently from the management people in business and government environments that he was used to work with.