You were already close to it when you said

can result in people answering a question that's already answered on the other site

Making someone answer a question which had already been answered somewhere else, would be a sign of disrespect (kind of "I don't mind if you waste your time"), and this feels to me impolite. Sorry if I was not clear with this.

What matters here is that the OP now seemingly understood the case, and this is a good thing. I remember well that when I started using newsgroups long time ago, it also did not occur to me that crossposting can be annoying.