Au contraire. One need not, for example, follow every single belief system that is polytheist to know that it is wrong by virtue of there being only one God. Therefore, it’s been narrowed down to possibly 3 belief systems. Of those, 1 pretty much contradicts the other 2, so that narrows the possibilities even more, doesn’t it...
Without studying every polytheistic belief, how can you deduce that they are all wrong?
Some protestants view Catholicism as a form of polytheism because they pray directly to Mary and other saints (or in a more polite sense, they are "monotheists with polytheistic tendencies"), so there's not even an agreement within Christianity itself.
...so that narrows the possibilities even more, doesn’t it...
Not all. There's thousands of different belief systems within monotheism.