Because, there was a vague, confusing, philosophical use of the term "energy of
motion" that predated Newton and he wanted his audience to connect. People also
used the term "momentum" and often used the two terms indistinglishably.
Newton's work was clear.
Newton did his calculus in Principia in a rather implict way so that it
would look more like proofs in euclidean geometry. He did this because he was
expecting to be criticized for his new tool of calculus ( fluxions).
By using previous terms, he made his work less radical appearing.
But, the intelligent reader of his time understood how radical it was.
Good historical question!
Although, Newton derives it as a first integral of the equation of motion, he
never uses the term "first integral" for that would be using calculus (
fluxions) in an explicit way. He thought people like Hooke would have villified