I expect the Cabinet will still represent a single vision, it will just be the vision of the leading coalition instead of the vision of the President. Because the new Electoral system would make everyone hyper aware of how fast their political career can end, and therefore it would eventually be considered political suicide to be an obstructionist unless you are absolutely sure that is what your base wants. The idea is that because nobody likes a government that can't get things done people will punish politicians who make that impossible.
And even if they don't this ability to check executive orders is the only power that the Cabinet as a whole has, the rest of the powers belong solely to individual Cabinet members and therefore they will likely get there individual jobs done regardless.
It would interfere with the separation of powers in the sense that the president would have a harder time passing legislation, but passing legislation is the job of the legislature anyway. As far as I see it the separation of powers has already broken down in the executives favor, this would just be correcting for that.
As for your point about the referendums, I agree that that may have been an over correction. The main thing I was worried about was a common occurrence in my state of Texas, here the state has to hold a referendum everytime it wants a constitutional amendment, which is often because of the way the Texas constitution is written, however because so few people vote in state elections they usually pass with only a few percentage points of the population in favor of them. But yeah like I said, in hindsight I may have over corrected for that problem.
