What is the biblical support for the practice that only ordained church leaders should administer the only sacraments of baptism and the Lord's Supper?
As St. Paul explains in his letter to the Romans, you are certainly not the first to ask this question ;-)
For as in one body we have many members, and all the members do not have the same function. Rom 12, 4
“Sacraments” are intimately related to “Church”. In Scripture you will find that Jesus himself gives the Holy Spirit to his disciples so that they can give it on. By doing so, He institutes the sacraments and gives authority to the Church to administer them:
Jesus said to them again, "Peace be with you. As the Father has sent me, even so I send you." And when he had said this, he breathed on them, and said to them, "Receive the Holy Spirit. If you forgive the sins of any, they are forgiven; if you retain the sins of any, they are retained." Jn 20, 21-23
This is an example of how the administration is preceded by an ordination:
- He sends
- He gives the Holy Spirit
- He gives the power to forgive sins or not
Note that you could apply the same to Jesus Himself: “As the Father has sent me”.
Another interesting phrase is “if you retain the sins of any, they are retained”: I like to think that Jesus wants these disciples to make sure that everyone gets a chance to receive the gift of forgiveness.
I hope this helps, feel free to contemplate the whole chapter (book) of both excerpts, it often helps to get perspective.