In the U.S., in mathematics, by 2016 (as opposed to decades back, perhaps), I think it's by far most often the case that the only real "filter/gatekeeping" for grad school is admission in the first place. There are "qualifying exams" and/or equivalent "require courses", but these are rarely used as filters; rather, they are devices to induce students to study more broadly than they might have otherwise. Yes, at some point there is the entirely-different enterprise of thesis-writing, and skills relevant to timed exams have very little to do with thesis-writing skills.
Since the qualifying exams and/or required courses are meant to encourage a bit of breadth, and to make a case for the utility and sense of that, it is reasonable to be coooperative with students in such situations, rather than be their adversary or skeptic. In particular, giving many good sample-solutions, illustrating the virtues of the ideas being discussed, is surely a good thing. Give archetypes for "expert" solutions.
Further, one might argue that in basic graduate mathematics the list of key ideas is really not so large, and part of what we should convey/sell is indeed the simplicity of things when seen from a slightly more sophisticated vantage. Therefore, I do not want to contrive clever problems that obscure the simplicity I'm trying to claim/show.