Pretty sure the whole team is telling Burke to shoot the ball most of the time since no one else on the team really wants to shoot the ball, especially when Hayward and Hood are out.
You can blame Burke all you want, I've soured on supporting him as of late, but you have to recognize he is being asked to shoot a lot. He does make a lot of bad decisions out there, but the team is asking him to handle a larger portion of teh scoring load than he is able to handle. Instead of backing down, he at least tries. More than you say for Exum at this point.