We don't know what happened exactly. We know that a huge part of the budget went into the development of the Fox Engine, not the game directly, then Konami shifted focus and deemed AAA games not profitable enough. We don't know how advanced was the game development when Konami decided to cut the money. All we know for sure is that the game was supposed to be bigger than what we ended up with. We'll never know the whole story.
Major time spent developing this game was on the engine and the plan was to reuse this engine on other Konami properties and developing more Kojima games. Also, for sure Kojima is one of the few people who can get away with the time it takes to make his games, but he is also one of the few people in the gaming industry who is doing what he is doing. With the cinematic, the wild story and even though MGS5 didn't have a wild story. Once you start to think just how much engineering and time spent on creating that incredible smart AI, the open world and an engine that can handle all this, its easy to see why it took so long.