Oh yes, I agree completely that wikipedia is not a horrible place to start. I do use the Notes / References whenever I go on wikipedia to double check the reliability of the information. But I do also notice that many times the references will point you to books. They don't always point you to this great primary source entirely online; at least my experience is that this is hardly ever the case, others' might differ of course.
So yeah, I do use the internet a lot to search for information. But in the end, the internet still take me back to the library.
Ah, you're looking at the wrong part. Go down to the "citations" part. Any decent article that might actually be the topic of an assignment will have five to ten times more "real" citations from primary sources than any teacher ever assigned me to have in school.
Wikipedia is still a "cheat code" for school assignments, you just have to use it right. Copying and pasting Wikipedia text is wrong. Following it to primary sources is hard to call "wrong", harder to detect, and, honestly, at the point where you're yelling at the student for getting your primary sources from one place and not another you're crossing dangerously close to "You did the assignment too efficiently, do more busy work" rather than "I want you to learn something from real sources". Students are very sensitive to that sort of message (even if only subconsciously) and we send the "do more busywork" message pretty loudly as it is; we don't need to amplify it any further. (I'd say, if the assignment has become too easy, make the assignment harder by making it actually harder, rather than forcing inefficient techniques.)
(BTW, my "write a paper that could be copied from Wikipedia" period ended well before Wikipedia existed, but unless they've radically changed the types of papers that are assigned, this is still essentially the optimal approach in terms of time.)