You might say also that the cliche that God is love makes sense only if Yahweh has a female consort, which he used to have in the ancient Israelite pantheon (Asherah). But that consistency got lost along the way.

Alas, the simpler explanation is the more cynical one. The Trinity became popular for the same reason the universalizing Church declared Jesus's birthday to be on the day of the winter solstice, to appeal to pagans who worshiped the sun god.

Time and again, as a syncretic movement that combined Jewish monotheism and morality with Roman polytheism and institutions, Christianity used the latter to sell the former. So polytheists could be happy with the Trinity doctrine as a halfway house, lending their support to the Church even if they didn't fully embrace monotheism. As the universal faith, Catholicism was meant to be all things to all people. Nothing becomes that popular without compromises.