Can a loving, true friendship between a man and a woman exist without physical attraction or sexual desire? Is this kind of love impossible?

Absolutely there is such a thing as true friendship. Physical attraction and the “love” it produces is an elementary stage of higher love and can help lead to it. In the varying stages of later levels of this higher love, the two people involved are self-completed and therefore don’t look to one another to fulfill a sense of incompleteness, however manifested.