Curbing access to certain game elements for story/player development can be annoying for some players who like to explore the game world from the beginning. Many get intrigued by visible but inaccessible game elements which they will get access to in the future, but they would like to experience them immediately. This "Carrot and Stick" approach, although rewarding for some players can be punishing for some. Such players who feel that they are being teased may avoid the game entirely.
Examples[]
1.Grand Theft Auto: Vice City[]
GTA Vice City Closed Bridge
In GTA:VC the player cannot access the other half of the map. It only opens up after a certain mission is completed. Also in GTA:VC your character cannot swim and dies if he falls into the sea. Hence there is no direct way to access that part of the map before the game allows you.
2. Witcher 2: Assassins of Kings[]
In Withcer 2, it creates a very beautiful game world with varified terrains and multiple establishment. Yet the player can not get access to many of them. Even worse player can not get to a hill or get cross a river or a narrow cliff, and you are only allowed to climb or jump at certain locations as if you are programmed to do so. This, to a large extent, contradicts its claim to be an open world game.