They keep track of $100 down the hole because:
The casino manager is going to ask the pit boss at the end of the shift, "HOW MUCH DID YOU DROP"?
He will then calucate the fills and know exactly how much the shift won. Because the GM might or might not ask him the question. If the GM asks, the CM does not want to look like, he does not know what is happening.

2nd reason:
If there is a player winning or losing big, the CM is going to ask the pit boss, "HOW MUCH." The pit boss better have an answer.

Actually this is a holdover from the old days. Computers now issue daily "Flash Reports" with all information as soon as the hard and soft counts are completed.