As noted, almost any 2 tier green can create that situation. I recall reading here that the minimum rollout for a putt coming over a one foot ridge is 14 feet, so any cup within, say, 6 feet of the base of a tier means you can only get within 8 feet. Similar situations exist when you go over a green.
I would say there can be a place where you can't get up and down. I call it strategy, knowing where to not miss. I do recall working with tour pros and low handicappers who would walk around a green in the dirt with one question...."What if I hit it here?" So, they obviously believe that they should be able to get close to the pin from anywhere. I understand it. The point of golf is to get the ball in the hole and hole locations where you can't do that are sort of counterintuitive to most.
Jim Colbert used to have me put in holes where there was a pond one side, and a fw chipping area on the other as a tempting bailout, with the green sloping to the water steeply (i.e., 2.5% or so) to make it tricky to hold the green from the bailout area. I'm not sure I agree with that......at least the steep slope where you could pond the ball from the bailout. IMHO, a bailout usually ought to let you on the green. It's more exciting to have a chance to recover par over making a certain double when playing safe.
It's part of the old RTJ easy bogey hard par mantra. It also depends on what your design brief is. If it is a public course, maybe there shouldn't be too many if any intentional places where you miss and the hole location means that a large number of C and D players may take 5 or 6 putts is to be avoided for speed of play reasons. There is a reason supers don't put cups on top of mounds, etc.
For public courses like that, I would compromise, and maybe put a few greens where the major defense/challenge is putting. However, a steady diet of that would likely tee off too many golfers, but they see a few as memorable variety.