Why?

Because it helps identify relationships.

"Sakura" is also the same word for cherry blossoms. So when Tomoyo's favorite flower is a sakura, you know how much she likes Sakura.

"Nadeshiko" is also the name of a flower. So when Sonomi's favorite flower is a nadeshiko .... well, you get the idea (and you begin to understand that Tomoyo's fascination apparently runs in the family).

Some of the other relationships aren't as obvious to a non-kanji reading audience. Kanji are the really complex characters that are taken from the Chinese language and used by the Japanese as 1/3 of their written language (the other 2/3 begin hiragana and katakana). Each kanji has 2 ways to pronounce it, and what it means depends on what characters are around it. But enough with the language lesson.

Just so you know, different parts of the first names of the Kinomoto family members that are represented by kanji are also the names of flowers. The kanji that begins Touya's name is the same as peach. That's why when Sakura thinks of peach blossom is Episode CCS#25, that leads her to think of Touya.

The kanji that starts Fujitaka's name is the same as wisteria, which is why Nadeshiko's favorite flowers are sakura, peach blossoms, and wisteria.

In the Victorian era, a "Language of Flowers" was developed, where each flower, and each color that flower could bloom as, had a different meaning. People would give each other specially created bouquets of flowers that were really messages of their feelings for each other. The person receiving the bouquet would understand the message by looking the different colors and types of flowers that were in the bouquet, which were known as "tussie-mussies".