Yes it's important to remember that things were not great before Havelange. He exploited a mess that grew during the Rous era. Dozens of African countries had become independent and FIFA membership rose dramatically - Rous and co were slow to react and assist. At this time FIFA was basically like a gentleman's country club, and African FAs had to pay hundreds of Swiss francs per years to remain members, with little tangible "reward" other than the right to say they were members. Compare this to the massive handouts and coaching assistance etc provided by FIFA in later years. This was the biggest benefit of the Havelange exploitation of the game. But let us also remember that he was corrupt from the beginning - many votes in Havelange's election in 1974 were bought with corrupt payments of Adidas money.
Yes, FIFA did need a kick up the ass before Havelange. As Piet says, 1966 alienated much of Africa and Asia due to under representation, but also South America due to perceived referee bias. South American FAs were already considering exiting FIFA and forming a breakway group before Havelange was elected. Rous's backing of Taiwan and to some extent Israel, and his dabbling with South Africa were also vote losers. So things had to chance, and anybody clever with an alternative vision (especially one involving $$$$$$) had ready support. Football was being undersold and was ripe to be milked by big sponsors and TV. With Havelange as leader, it was actually Blatter who oversaw a lot of the programmes to pump money into Africa etc. And it was all the same tactics which kept working for Blatter even up to his last election.