Why doesn't Srimati Radharani wear tilaka?
Experts in Vaishnava culture say that "tilaka" is the name for any mark on the head made of clay and having sacred connotation. So, perhaps the actual question is, "why doesn't Srimati Radharani wear Gaudiya Vaishnava tilaka, in the style worn by followers of Chaitanya Mahaprabhu?
Bhakti Vidya Purna Swami told me that the tilak that we wear is "Krishna's tilaka," and that Radha wears "Radha's tilaka." Traditionally, a woman places kunkuma on her forehead, and Radha also does so. In the shastra, scripture, she is described as having "a dot." This has morphed into bindis, which are pasted on the head for decoration, but this is not the same thing. Maharaja (BVP Swami) said that the kunkuma powder has an effect on the chakras of a woman and makes her peaceful.
In his book Teachings of Lord Chaitanya, Srila Prabhupada says, "the mark of tilaka on Her [Srimati Radharani's] forehead is Her fortune." (Chapter 31). So She does wear tilaka, although it may not appear like the kind worn by Krishna's other devotees.
But really, this question is like asking "Why is Krishna blue?" Ultimately the answer is, "Because He is!" All we know of Srimati Radharani is what is described in the shastra. And Her superexcellent qualities are only very minutely described.
More about tilak:
Article: Tilak, the mark of God, by Rohininandana dasa
Video:Why do Krishna devotees shave their heads and wear tilak?, with Ravindra-svarupa dasa
Video: How to put on tilak, with Nityananda Chandra dasa