Despite Rarity, being annoyed at her parents’ uncultured ways, she appreciates how they went from rags to riches and how they gave Rarity and Sweetie Belle good oppurtunities in life. The Belle family were by no means as rich the Rich family but they still had a great amount of money.
However she was always frustrated how they didn’t act too posh, and how they were just satisfied at being rich. Rarity wanted to go beyond mere riches, she also wanted high culture.
She even wrote a letter to the mayor when she was a filly for all ponies to speak the Canterlot accent like her tutor taught her.