Speaking of the Piccadilly Line, there was a classic example of stations closed specifically because they were felt too near to adjacent open ones. In central London all of York Road, Down Street and Brompton Road were closed in the 1930s, it being justified that they were little used and the next stations each side were adequate. This notably applied where station entrances with lifts vertically down were replaced with new entrances a distance away with slanting escalators to the platforms - the new entrance could be a good proportion of the way towards the next station.
In passing the Piccadilly, a deep-level tube, was originally built with a lot of close-together stations; sometimes the next one is visible along the tunnel from the previous one's platforms. Always amuses me when nowadays there are arguments for years about station positioning on new lines and how each one may add hundreds of millions of pounds to the project cost, when the original Piccadilly investors seemed to quite happily dig down for one every half a mile, sometimes even less.