Do we teach for any reason besides pleasure?
Humans can focus their attention away from their present moment into the past and future. We develop a sense of identity. We can reflect back and learn from our experiences. We teach others what we learned.
Someone adapted to a Nazi concentration camp becomes apathetic and almost entirely focused on food and survival. There is no need for sex. Once a man's basic needs have been met, he can aspire to higher level goals, like art. That's not to say prisoners never displayed artistic expression, just very seldom.
Those who are doing excellent design work are making things to be workable, useful, and desirable. We have life, justice, and fun. (Call it life, liberty, and the pursuit of happiness). Is that it?
Now that we've improved our survival fitness, can higher level aspirations emerge from culture?
I still prefer the title "What is culture for?" more than "What is the purpose of culture?" By receiving the verb we sound like a victim.