There is value in duplicating documentation even wholesale and unmodified, if different duplicates are easier for some people to find and use, but there's even more value in "duplicating" documentation by presenting it differently, which is what SO is doing, even for many questions that you believe to be trivial. The more the merrier, if you ask me.
Now, of course, it would suck if you felt lazy people with already-answered questions were wasting your time. Then I would understand your point of view. But the fact is that you just don't have to answer their questions. If somebody else does answer it, well then that person probably didn't feel like it was a waste of time.
Presumably SO wants to maximize its readership. What I've seen is that they allow any programming question, even of trivial nature, as long as it's objective not subjective. I like that and think it's a good way to maximize readership for objective stuff, because I often google for trivial things. For example, Powershell if/else/elseif syntax, if I haven't used Powershell in a while. I just found the syntax on SO within 10 seconds, with an example I can copy/paste/modify. I bet a lot of other developers use SO like that too, and I bet it's largely the reason people put trivial questions on there. My motivation is efficiency. Being efficient can be construed as lazy I guess!