It seems to me that polytheism is easier to grasp, and so tends to be popular by default, while monotheism is easier to defend, and so tends to emerge when it needs to be defended (whether from political opponents or your own knowledge about reality)

I'm not so sure about that. We have much more exposure to attempts to defend monotheism from polytheism or atheism, so it may appear easier, because there's a glut of arguments coming from that direction. That could just be a historical accident though. Maybe we could have ended up quite easily in a world where the most popular religions were offshoots of Chinese syncretism, and we'd be much more familiar with arguments defending polytheism.

Monotheism has sprung up in polytheistic cultures, but in some cases we've also reinterpreted the work of old philosophers through monotheistic lenses. A lot of classical Greek philosophers framed their arguments in terms of "the gods," who're now interpreted as talking about "god," and the idea of omnipotence wasn't really in popular circulation. The closest I know of any Greek philosopher coming to monotheism was Aristotle with his Prime Mover, but it was Aquinas who reinterpreted this as being about God. To Aristotle, the Prime Mover was more like a basic energy principle behind everything. The gods came from it, but it wasn't a being so much as The Stuff that Makes Stuff Happen.