Why monotheism supplant polytheism as a Dominant Institution of Churches

I am curious why monotheism succeeded at the particular time it did. Was it inevitable, or just a potential occurence? I'm not asking for religious information as such, I am more interested in the historical context that gave rise to monotheism as the dominant form of religion we know today.

TL;DR: Christianity offered unique benefits at a time when they were uniquely appealing while locking out other religions. The fact that there was only one god involved as opposed to many is simply a coincidence.

I think that monotheism, as such, is a bit of a red herring. What largely supplanted Classical religions was, first and foremost, Christianity, with Islam coming along later to mop up what was left. Judaism, for example, was never a widespread faith, nor did the occasional period of monotheistic-ish religion in Egypt really catch on. The fact that Christianity and Islam happen to profess a single deity (more or less; saints and the Christian trinity are a bit of a gray area) are secondary to what made them appealing and eventually dominant.

Christianity came along at the same time as a batch of other "mystery" religions, as opposed to earlier "votive" religions. In votive religions (and many other forms of polytheism), religion is, for lack of a better word, transactional. You make the right prayers at the right time, you make the right sacrifices, and the appropriate gods look on you favorably and grant you the fairly specific favors you ask. However, it was all very external.