I liked the part about delaying the negotiations until Friday in (I think) Haiti, because they realised a lot of kidnappers just wanted money to blow partying on the weekend. They got away with paying a lot less.

Police/authorities want to do that because (perhaps) there is a connection between crime and terrorism. Meaning that, if you pay $100m to the kidnapper, 50% of that amount will end up funding <insert terrorist org>. They want to drain this to the lowest possible amount.

It seems to be a necessary part of the strategy though as the negotiation also helps to delay and buy time for escape/rescue.

They sometimes paid the amount. In some countries that was probably seen as a better plan. It probably depends how loose the cannons are.