"Why is it "poeta" and not "poeeta" in Latin?" This question occurs in the Harvard University Catalogue of 1872-73, but I haven't been able to find the answer. The reason I would expect "pœeta" is because it comes from Greek ποιητής poiētēs, and Greek οι is usually taken into Latin as œ.
I looked it up in Lewis and Short and Elementary Lewis using the Perseus Online Latin Dictionary, but the relevant sound changes were not explained there. Unfortunately, I do not own a Latin etymological dictionary.
At first, I had an idea it might be due to some kind of aversion to "double ee," but there are words with æe like præemino and haliæetus (that last one is another loan from Greek ἁλιαίετος haliaietos).