Complexity for its own sake is the first line of defense against lower-class parvenus like us.
Also, providing an increment for moves 61+ prevents late-game time scrambles which might otherwise persuade the players to seek safety in an agreed draw. With an increment, each player (and particularly, the player with the advantage) is guaranteed to have at least 15 seconds to find the proper way to press his advantage.
It is not uncommon that time control looks something like:
"The time control is two hours for the first 40 moves, then one hour for the next 20 moves and then 15 minutes to finish the game with a 30-second increment from move 61 onwards"
What is the point in all these complexities? Why not just give each player 2 - 3 hours, plain and simple?