It's always seemed a bit odd to me. The best explanation I can think of is that it's a reference to makeup, which is itself (sort of) transformational. Just wondered if this is something Takeuchi ever explained somewhere.
TL;DR: Because the target audience for the show are girls. And girls are supposed to like makeovers.
An excerpt from the book Millennial Monsters: Japanese Toys and the Global Imagination (Anne Allison) (emphasis mine):
In a property like Sailor Moon, these two words [romance and fantasy marriage] blend in a story line that incorporates both fighting and romance, (...) however the text still belongs in "girls' country" (...).
Girl heroes have powers rooted in magic or otherworldliness, they fight to help friends, their weapons double as fashion accessories, a princess or spirit empowers them, they "make up" when transformed, and "love" is their keyword. (...)
When girl heroes morph, however, the process is more a "makeover" than a "powerup". Apart from empowerment, that is, transformation also beautifies girls, fostering personal attractiveness, romance and dreams.
We can infer that the "make up" magic word in Sailor Moon is used to foster the identification process between the audience (young girls) and the characters.
In Sailor Moon Crystal, the protagonist is 14 years old. From the same Wikipedia article:
The audience is intended to mostly identify with the protagonist.
So, there you go.
This answer also answers: "Why is Tsukino (sailor moon) 14 years old?"