A lot depends on the implementation of Fate/the type of aspect it is, and the story that is being told in the creation of the character.
Type of Aspect
In some uses of Fate, all aspects are the same- no aspect is more important to the creation of the character than the other. In others, there is a High Concept or some aspect that to a large extent defines the character. Making that a multi-faceted concept so that it connects to the character in most situations is totally in line with the purpose of that aspect.
Telling of a Story
Aspects define what makes a character unique. To do so, they describe the core of the character and tell the story of the character. I think that many people focus on the what of the aspect, i.e. the utility and focus of it in game, rather than the why of the aspect, i.e. the storytelling part. If you look at an aspect, it should be evocative and tell a story.
To take a look at that in the text, I'm going to use the text of the Dresden Files for an example, i.e.
Here are a few “good—better—best” examples:
While the Tepid and Toasty examples are good and decent aspects, the Fuego! one tells a story. They evoke thoughts just reading them, and don't have to be explained.
To me, Gnome Illusionist is probably Toasty, as is In Search of Power and Prestige. However, Gnome Illusionist in search of Power and Prestige is more evocative. It tells me that the Power and Prestige that he is in search of is related to him being a Gnome Illusionist - not just any power and prestige. So I don't just throw at him the ability to seize power over a sleepy hamlet- but the ability to find The Lost Tome of the Greatest Gnome Illusionist ever (TM).