Because nowhere in the Bible can you find anyone calling Him that.
I think people call him Papa Jesus because they are trying to describe a relationship that feels warm and relatable. I understand the point. Still, the Bible doesn’t call him Papa Jesus and the reason is theological. Jesus is the Son, not the Father. Calling him Papa is not consistent with what the Bible teaches about the Trinity.
In Filipino culture, the word “Papa” has fallen into disrepair. It doesn’t just refer to biological fathers now but also to good looking guys on TV. We all know that the “papa” anyone would use on a strapping young lad is not in the same league with what Christians have in mind for Jesus.
Centuries ago, Greek Christians had the same dilemma when they were trying to translate the Hebrew “Jehovah” to Greek. They knew that the word for “god” was “Zeus,” a name which was already taken by the well-known Olympian mythological figure. To avoid confusion, they discarded the famous Zeus and opted for the little known word “Theos.” That was a good move. The Greek Christians didn’t want to use a word that is already loaded with cultural meaning. Maybe we can do the same today, not just for cultural and linguistic reasons but because we want to honor Christ by calling Him by his preferred Biblical name.
Edit: A Facebook comment pointed out that in Isaiah 9:6, the Messiah is called Everlasting Father. John Calvin commented that the original Hebrew text literally means “Father of Eternity,” meaning, the One who founded, originated, and authored eternity. “Father of Eternity” is not a name but a character description of the Messiah, just as we say that Hippocrates is the father of modern medicine. His name is Hippocrates; he originated modern medicine.