Oil painting replaced other mediums in the Renaissance because it was more versatile. It was more colorful and it didn't dry as fast, allowing the artist to create a more natural painting by blending. This tool hasn't changed much from the Renaissance era, and is still used greatly today.
The purpose of oil paints have stayed the same throughout history, to create beautiful art for people to view. Although every artist's preference may be different, oil paint is extremely versatile and has been used for centuries by many.