Before the release of Fallout 4, it was necessary to release some other project in the franchise.
Recently, the head of Bethesda Game Studios spoke with Game Informer. During the interview, he talked about why Obsidian Entertainment became the developer of Fallout: New Vegas.
Todd Howard explained that this studio was actually "the only option." At that time, Bethesda switched to working on The Elder Scrolls V: Skyrim and the developers understood that the release of Fallout 4 would definitely not take place in the near future.
It was necessary to fill the resulting gap with something and then they remembered Obsidian. Bethesda knew these developers well. The studio had previously worked in a similar mode on Star Wars: Knights of the Old Republic 2 (quickly created a sequel to someone else's franchise).
Todd Howard noted that the only instruction given to Obsidian was to focus on the faction system in the gameplay.
Obsidian's lead creative designer John Gonzales explains:
The studio had Fallout DNA - there were people who worked on the original game, as well as on the second part. What made Fallout: New Vegas special was the focus on gameplay with choice and consequences. This is a very Obsidian-style game. The idea is to allow the player to have a huge impact on the story, to control it.