You are maybe just having crap luck, I've received 6 total exotic engrams from publics, since last Tuesday.
RNG just doesn't like you or something.
Today's patch should correct your problem, they have actually made getting stuff super easy with all the changes. Exotics will rain down from the sky.
Bungie is so confused about what a large portion of their dedicated players what from this game, it's sad.
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Zavala, Shaxx, and Tess are all selling a new token that gives everyone stuff, and Xur is selling 3oC again. It's funny you say Skyburners is all you are getting, I read a post earlier from someone who can not get it, and claims it's drop rate is rigged.