Characters having a distinct and consistent look is just how things are done in videogames. No-one questions why Mario always wears his blue overalls and red hat, or why Ryu always wears his white gi; its the look that the character is known for.
And yet the Mortal Kombat characters are tweaked on a regular basis. Sub-Zero famously appeared without a mask for the first time in MK3. The characters don't drift too far away from a central basic design because the developers understandably want to maintain a certain level of consistency in their appearance, but they're not afraid to muck around a bit.
Again, I'm not suggesting Morrigan be drastically overhauled. But I see no good reason not to experiment with her clothing a little just for the sake of variety.
These characters aren't the Flintstones or the Mario characters where trying to apply this sort of logic would be pure folly. They're meant to be somewhat rooted in reality. After all, we spend a great deal of time here dissecting their personalities and motivations, and arguing whether or not something someone said or did was in character. But when it comes to the question of a character electing to wear the same clothes for a decade, the answer is "Because Mario?"