My guess is that Jesus was trying to protect the healed from the Pharisees. Jesus would have foreseen that the Pharisees would persecute his disciples, or at least cast the testifiers out, like they later did to the blind man.
John 9:18-34
18The Jews
a did not believe that he had been blind and had received his sight, until they called the parents of the man who had received his sight
19and asked them, “Is this your son, who you say was born blind? How then does he now see?”
20His parents answered, “We know that this is our son and that he was born blind.
21But how he now sees we do not know, nor do we know who opened his eyes. Ask him; he is of age. He will speak for himself.”
22(His parents said these things because they feared the Jews, for the Jews had already agreed that if anyone should confess Jesusb to be Christ, he was to be put out of the synagogue.) 23Therefore his parents said, “He is of age; ask him.”
24So for the second time they called the man who had been blind and said to him, “Give glory to God. We know that this man is a sinner.”
25He answered, “Whether he is a sinner I do not know. One thing I do know, that though I was blind, now I see.”
26They said to him, “What did he do to you? How did he open your eyes?”
27He answered them, “I have told you already, and you would not listen. Why do you want to hear it again? Do you also want to become his disciples?”
28And they reviled him, saying, “You are his disciple, but we are disciples of Moses.
29We know that God has spoken to Moses, but as for this man, we do not know where he comes from.”
30The man answered, “Why, this is an amazing thing! You do not know where he comes from, and yet he opened my eyes.
31We know that God does not listen to sinners, but if anyone is a worshiper of God and does his will, God listens to him.
32Never since the world began has it been heard that anyone opened the eyes of a man born blind.
33If this man were not from God, he could do nothing.”
34They answered him, “You were born in utter sin, and would you teach us?”
And they cast him out.
