Did any Christian philosopher explain why monotheism is better than polytheism as they rejected polytheism and accepted monotheism?
Xenophanes criticized polytheism. In his view, there could exist only one god in one reality, independently of us human beings. It was the time that the existence of such a reality became popular. This was carried on to the reality of the world of the gods. It was driven to the extreme by Xenophanes. Not only was there one such reality but there could be only one god also. And it couldn't be imagined, for who knew what he/she/it was like (an attitude as seen nowadays by most scientists). His god was an omnipotent and omniscient superbeing.
This idea moved on to Christian religion. There is one god and it's forbidden to picture him (there is a taboo on this at least, contrary to Islam, where it is forbidden explicitly). He sees everything and knows everything. That's the absolute truth. I don't think there are any Christian philosophers who disagree. Christianity is better because it corresponds to the Truth. They wouldn't be true Christians!
Of course, it depends on the philosopher, and there are a lot of them. Look here. They may not argue that monotheism is better than polytheism, but they certainly deny the reality of the gods in question. If they think it's better then the reason would be the reality of monotheism. It's for your own good to adhere to monotheism. People representing the Christian church of Christianity (so not the philosophers) don't forbid people believing in more gods. But they will try to get them to their side (not the other way round, maybe because God is one of their gods already, where "God" is a name of the entity and "gods" are the (God-like) entities themselves).
The best and earliest example of a historical figure who argued for monotheism and against polytheism, was Paul of Tarsus-(i.e. Saint Paul). The entire second half of The New Testament-(i.e. Acts and Epistles), was authored-(as well as co-edited), by Paul.
During his lengthy travels throughout the Middle East, Asia Minor, Greece-(and even during his final days in Rome), Saint Paul preached the Christian message to the pagan populations of these lands and countries. Part of his sermonizing language included aggressive critiques against polytheism, especially, idolatry. While Saint Paul did persuade many audiences in these lands, he upset and even angered many audiences as well, including the Greek and Roman Theatergoers in the city of Ephesus, the Magistrates in Athens and the Emperor Nero...who had him executed.
The Second half of The New Testament, is perhaps the best and earliest example of a Moral Messenger who argued in favor of Monotheism, while equally criticizing the falsity of pagan idolatry and piety....to largely pagan audiences.