But I wonder why was this oral transmission found through so many different cultures of a man in an ark gathering all the animals surviving a great flood?
How many and which cultures?
Without making me pick through them, which ones actually have all the elements that the OP speaks of? I'm aware that many cultures have flood myths. Many cultures where floods happen, anyway But I'm particularly asking about cultures with the "gathering all the animals" into an ark and saving them part of it in their story?
Noah in the Old Testament (obviously)
Gilgamesh in Mesopotamia
Deucalion in Ancient Greece
The Celts had a story involving a ship, but no mention of animals
Dwyfan and Dwyfach in Ancient Wales
Ancient Sumer had a flood story that looks separate from Gilgamesh
Zoaroastrians had/have a flood myth
Maasai in Africa
Flood myth in Southwest Tanzania
Yenisey-Ostyak people in Siberia had no boat, but people and animals saved by clinging to logs
Kamchadale people in Siberia had a boat but no mention of animals
Altaic people in central Asia
Tuvinian people near Mongolia had a boat story, with no mention of animals
Buryat people in Siberia
Sagaiye people in Siberia
Hindu mythology has a flood myth
Karen people of Burma had a flood myth with a boat but no mention of animals
Maori story had a raft but no animals
Hawaii had a flood story with a boat, no explicit mention of animals, though it is implied.
Sarcee tribe in Alberta, Canada
Michoacan people of Mexico
Trique people of Mexico