Paul’s handkerchief and the physical medium of miracles?

A number of miracles in the New Testament are not wrought by someone just praying. Instead, there are often physical intermediaries. One example is Paul's handkerchief, which could be used to heal people in absence of Paul himself. Another is the lady touching Jesus' robe. Jesus also used mud in the eyes of the blind man. Even when other physical objects are not used, often the healer lays hands on the person being healed, which is still a physical object being used as a medium. One could even say the words used in a healing prayer are a physical medium, since the words already exist in the person's mind, and God can read everyone's mind, so aren't strictly necessary to exhibit a person's intent to heal. Why are physical mediums of one sort or another used in the enactment of all the miracles? Why don't people just think the miracle into existence?