First, let's look at the origin of the term "study". In art, a study is
a drawing, sketch or painting done in preparation for a finished piece, or as visual notes. Studies are often used to understand the problems involved in rendering subjects and to plan the elements to be used in finished works, such as light, color, form, perspective and composition.
Endgame studies in chess got that name because they try to render a given theme or idea as clearly as possible, without distractions or irrelevant parts.
A part of an existing drawing may be interesting, but it wouldn't be called a study.
Here's what Wikipedia says about endgame studies, emphasis mine:
Composed studies predate the modern form of chess. Shatranj studies exist in manuscripts from the 9th century, and the earliest treatises on modern chess by the likes of Luis Ramirez Lucena and Pedro Damiano (late 15th and early 16th century) also include studies. However, these studies often include superfluous pieces, added to make the position look more "game-like", but which take no part in the actual solution (something that is never done in the modern study). Various names were given to these positions (Damiano, for example, called them "subtleties"); the first book which called them "studies" appears to be Chess Studies, an 1851 publication by Josef Kling and Bernhard Horwitz, which is sometimes also regarded as the starting point for the modern endgame study.
So in modern times they are as streamlined as possible and that is also when they started to be called studies.
As for the link with computers, that is very interesting. Here is a link to a Powerpoint presentation "Composing chess studies with the computer", unfortunately in Dutch only, by the precise people you'd want to have talking about that: computer chess expert and AI professor Van den Herik and GM Jan Timman, also famous for his endgame studies.
They explain that theoretically it is possible to have a computer program that can decide whether a study is correct (single solution) and judge its quality, based on a list of desired qualities:
- Successfully breaking heuristics
- Use of the weakest piece
- Using all of the power of a piece
- Giving more esthetic value to critical pieces [I don't know what they mean]
- Using a single "heavy" piece instead of several "light" pieces
- Use of themes
- Avoidance of obvious stereotypes
- Strangeness and difficulty do not lead automatically to "beauty"
A computer could then assist a composer, or go through databases of games or endgame tablebases to find potential beautiful studies.
But, that program hasn't been invented yet.
There are tablebase positions that have single solutions (at least for a large part of the main line). They could qualify, but most people think they don't demonstrate a clear theme, for a human the moves look incomprehensible. Thus they fail as works of art.