Many games nowadays market themselves as open-world and play-as-you-want. However, many of them lack actual choice. For example, in Grand Theft Auto V, the player is often shepherded down these very linear story missions that include them killing a bunch of people. However, the feeling of an open-world game is completely the opposite, generally allowing freedom. Having this very binary system of "open world" and "linear story missions" is very jarring and disconnected. Allowing the player to choose the way they want to play in open world games makes things more consistent and more accessible so many players with different styles can play.
Fallout New Vegas gives the player almost unparalleled options to play the game. Most story missions have multiple ways to complete. For example, you can beat the entire game just by speaking to people and never firing your weapon. This lets people that are not good at shooting to enjoy the game. It also is in line with the consistent feeling of open wasteland freedom and exploration.