According to producer Yoshiaki Koizumi. Pauline was originally conceived as the princess of New Donk City, but the idea was later scrapped and she became the mayor of New Donk City instead.

"In the past we used to have a game taking place in a city, and Mario also appeared in it(which pointed towards Pauline). At first they wanted to make her the princess of New Donk City, but the world setting of that city doesn’t have princesses. That’s why she became the mayor instead.”
Contributed by CLXcool