Agreed. But then we need to ask, 'what kind of experience?' To which I respond: Not experiences of happiness but of suffering, quite often suffering in silence.
I agree that no one can call themselves wise without experiencing the suffering that is part of this world. But can you imagine how lacking in true wisdom one would be if they never experienced joy, pain, sadness, love, loss, triumph-- the full gamut of human emotions and experiences? It takes much of a person's life to experience these, which is why truly wise people tend to be older.