
This answer comes courtesy of contributing expert Max Rubin:
This quaint practice harkens back to days of yore, when the only things protecting the casino’s bankroll from crooked dealers and wiseguys were the eagle eyes of even wiser guys suited up and manning the pits. The bosses had to keep a "sweat sheet," which told them how much money was dropped and who took the chips away from the table. This helped them keep a running inventory of wins, losses, and each table’s hold percentage.
Now that the casinos have sophisticated surveillance systems that can record every move and keep track of virtually every transaction forever (if need be), they still haven’t changed a single protocol! Why? Old habits die hard and most bosses still think (because that’s what they’re told) that their primary job is sweating winners and making sure that every black chip is accounted for.
That’s not to say that bosses shouldn’t watch the big transactions (dealers will occasionally make mistakes counting money/chips and the bosses have to log big cash buy-ins for the IRS’ pleasure), but if the suits were to spend more time having fun with the guests instead of worrying what to tell the big boss if a chip or two somehow made it to the cage without the obligatory and affirmative grunt every time a player showed up or wanted to leave, they might actually (gasp!) be able to create a more enjoyable gaming experience for their customers.
For more candid and entertaining insights into the world of casino management and how to get the most out of the system, check out Max's book Comp City, a guide to free Vegas vacations written by this former casino executive, and now in its second edition.