Blessed are the pure in heart, for they shall see God. (Matthew 5:8)
38 Then some of the scribes and Pharisees answered him, saying,
“Teacher, we wish to see a sign from you.” 39 But he answered them,
“An evil and adulterous generation seeks for a sign, but no sign will
be given to it except the sign of the prophet Jonah. 40 For just as
Jonah was three days and three nights in the belly of the great fish,
so will the Son of Man be three days and three nights in the heart of
the earth. 41 The men of Nineveh will rise up at the judgment with
this generation and condemn it, for they repented at the preaching of
Jonah, and behold, something greater than Jonah is here. 42 The queen
of the South will rise up at the judgment with this generation and
condemn it, for she came from the ends of the earth to hear the wisdom
of Solomon, and behold, something greater than Solomon is here.
13 Now when Jesus came into the district of Caesarea Philippi, he
asked his disciples, “Who do people say that the Son of Man is?” 14
And they said, “Some say John the Baptist, others say Elijah, and
others Jeremiah or one of the prophets.” 15 He said to them, “But who
do you say that I am?” 16 Simon Peter replied, “You are the Christ,
the Son of the living God.” 17 And Jesus answered him, “Blessed are
you, Simon Bar-Jonah! For flesh and blood has not revealed this to
you, but my Father who is in heaven. (Matthew 16:13-17)
These three passages show that God discriminates between those permitted to view a miracle (the pure in heart) and those who are not. The Bible surely records miracles viewed by unbelievers, but these passages show that miracles are more likely to be experienced by believers than unbelievers. If you had a video recording of a miracle, then it would immediately place it within the category of miracles that God permits nonbelievers to see. The Father will prevent any such documentation from being produced if the miracle in question is not one he wants to be broadcast.
Conversely, there is a way that news of miracles is permitted by God to be widely disseminated: word of mouth. On numerous occasions, Jesus healed a person but ordered them not to tell anybody about it. They ignored him. No harm came to them - God did not prevent them from sharing the news, even if it caused trouble for Jesus with the authorities.
Words have to do with faith, not sight. You have the choice to believe the one speaking to you or reject what they say. If you see a video of it, that could be a deep fake, but the tendency is to believe it. Little faith is required. God places a high value on faith as the means by which He acts in the world.
Concerning Paul's Damascus Road Conversion:
One commenter offers Paul's Damascus Road conversion as a counter-example. Paul was hostile to Christianity and yet witnessed a miracle. However, this objection may be answered. Paul's conversion did not begin on the Road to Damascus, but at the stoning of Saint Stephen.
When you break a jar of perfume, the fragrance fills the house. When you break a true believer, the fragrance of the Holy Spirit is poured upon all in the vicinity. While some may reject it still, this has a powerful effect. When Jesus' body was broken on Calvary, his spirit was poured upon the city and many holy people rose from the dead.
In the Book of Job, Job was a righteous man. When he was broken in body and spirit, the Holy Spirit poured out from him. His three friends rejected it, but a bystander, Elihu, was suddenly filled with the Holy Spirit and began to pour forth wisdom beyond his years.
So Saint Stephen, seeing the gates to heaven thrown wide open, cried out in prayer that God forgive the people who were stoning him. That direct connection to heaven and Stephen's sacrificial release of guilt on his persecutors allowed the Holy Spirit to flow powerfully through the crowd. It appears that it lodged in Paul's heart and began its work, culminating in the Damascus Road experience some time later.
I do not speak idly of this process. As a young man I visited a Christian woman at a nursing home who suffered horrible pain. I had suffered from depression for many years. However, after visiting Janet and praying with her and reading scripture to her, I left a changed man. For thirty minutes I bawled, so moved was I by her suffering. Then my tears were replaced with peace, and after that joy. The joy remained with me for a whole week, and in the midst of it, I finally understood the book of Philippians, in which Paul speaks of the joy that comes from emptying yourself to serve others. Jesus did that. Paul did that. And now I had seen a woman who retained her faith and witnessed to her family and all visitors despite being broken. At her funeral a few months later, another of her friends said, "When you were with Janet, it was like the Holy Spirit was pouring out of her."
It was that powerful, self-sacrificial spirit (originally derived from Jesus), not a miraculous vision of Jesus, that was the greater miracle - and that was a miracle of the heart that couldnot be seen.