Some time ago I heard of a photographer who takes only one image of wherever he goes in the world. One of those places was in Antarctica and was so remote that at the time it had been visited by less than ten individuals. There have been more people who have gone to the moon. Despite that and the immense difficulty of reaching the location, he still took just the solitary photo with his 5 x 4 camera, packed up his gear and left. That's right, he was shooting film so would not have known until later whether the shot was a success.
I have been trying to find out more information including the guy's name, but so far have not discovered the correct Google search term. There was a feature about him in Amateur Photographer several years ago, but I no longer have a copy of that edition.
I do agree that imposing an artifical limit on the number of shots that can be taken would be an exercise in frustration, especially in the digital age. Even with the cost of buying and processing 5 x 4 film, our Antarctica friend's actions seem rather extreme. That said, I do quite like the idea of taking just one film shot a week. I could use my dad's 63 year old Barnack Leica, which has manual focussing and no exposure meter. Last time I tried to shoot with it, I could not even load the film correctly. That would definitely add a certain frisson to the project.
I am starting to think about my photographic projects for next year. In many ways I have enjoyed the challenge of a 365 and certainly have made many worthwhile images which I would not otherwise have got, but I am not currently thinking of continuing it into next year. It has given me the impetus to take more photographs, so I am looking at ways of continuing to do this but without the impetus of making do with an inferior shot on slower days. I also have some other things in mind, but probably will not make a public announcement unless they come to fruition.