A few years ago when the federal dietary guidelines were being discussed, there seemed to be a growing consensus that nutritional goals and sustainable goals could be jointly achieved with a single diet. I pushed back some on that at the time (e.g., see here or here).
I ran across this paper by Zach Conrad and colleagues that was just published in PLoS ONE. The paper shows that there is unlikely to be a silver bullet diet free of trade-offs when multiple dimensions of comparison are involved. Here's from the abstract: