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My teachers at school and profs at University always say that Wikipedia is not a reliable source. Although it has less mistakes than famous encyclopedias.
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Rule-breaking posts may result in bans. >

nobody references Wikipedia because heavily instructed not to >

If only we'd be allowed >

LPT: Use Wikipedia and then scroll to the bottom of the article and cite the same sources they do. >

Everybody uses Wikipedia, the same way everybody uses a search engine or Google scholar. Its is a tool, that helps you find primary sources for your research. Tools are not referenced in your source list. 
Every Wikipedia article has a source list. Those are the ones you should use in your research, not Wikipedia itself. Wikipedia summarises things, but does not add anything new to a topic.
Hope that helps :) >

Why don't people reference it the same way as some summarizing studies? For example, systematic literature reviews. Is it because the articles in Wikipedia can be created by anyone, which is worse than highly credible scientists associated with some prestigious universities? >

I'll have to draw a blank on that one. Summarising studies is not something I've seen used at my faculty, but it is definitely possible that such sources can add value to research in other fields.