Part of that could work but for me the more interesting bit of any modern Godfather movie or any mob movie period would be how such people operate in a world of RICO (with very flexible standards of proof), Witness protection programs, incredible electronic/audio/visual surveillance, defectors/informants and declining (non-existent??) ability to prevent/soften prosecution.
What made the first two movies so great was that they mixed reality, history and fantasy so well. How would Vincent or any of his leaders operate in a world where that new associate could be an FBI agent, one of their friends got 60 years for waving hi to someone outside of a restaurant, and even the boss can't just call in favors from a Senator any more?
EXCELLENT points, Lilo. They couldn't really get away with the idea of there being no legal repercussions for the Corleones in this day and age.