I doubt the so-called "trine formula" only emerged in the 4th century. The Didache is thought to be a second century writing at the latest (not that I think people should use the didache), and it includes the expanded "name of the father, of the son, and the holy spirit"; so, that, to me is an indication that it was already being done that way to some extent before the trinitarians formalized their explanation of the godhead.
I think a lot of the emphasis on baptismal formulae is a distraction. it's like the "our father in heaven" prayer; it's not a prescription of exact words that you need to say, but it's a pattern that teaches you how to pray and what you should be asking for. I don't believe Jesus gave them rigid instructions to perform a ritual; and if you don't do it exactly right your sins won't be remitted- I think that's a fear tactic used by some organizations. The part about immersion into the person of Jesus Christ; that much is right- but it's not about the exact words that the baptizer is saying as he is doing a water baptism.
I think a lot of the emphasis on baptismal formulae is a distraction. it's like the "our father in heaven" prayer; it's not a prescription of exact words that you need to say, but it's a pattern that teaches you how to pray and what you should be asking for. I don't believe Jesus gave them rigid instructions to perform a ritual; and if you don't do it exactly right your sins won't be remitted- I think that's a fear tactic used by some organizations. The part about immersion into the person of Jesus Christ; that much is right- but it's not about the exact words that the baptizer is saying as he is doing a water baptism.
Neither is there salvation in any other. There is no other name under Heaven WHEREBY we must be saved. Acts 4:12