I'm not in academia, but I happen to find this type of question helpful,
when done well.
When questions make no sense and it takes a lot of effort to find out, I would agree that this is stupid and not testing for any real skill. But when questions are designed in a way to meet the knowledge level that is expected, I think this type of questions is good.
For example:
For what x does the value of function 1 / sin(x) become zero
This question leads you astray, but it is a genuine sign of understanding when the answer is "none". OK, this is not a real trap question, but it borders on one.
A more callous example, not a MINT question (not sure what kind of test would ask this question though):
A hotel room costs 400$ a night, breakfast not included. It is situated in NYC and the cost of a hotel room in NYC averages at 250$ per night. The average cost for breakfast is 50$. Hotel rooms in Manhattan average 500$ per night, while hotel rooms in Queens average 120$/night. In what part of NYC is the hotel located?
The answer one gives to this question could be quite revealing. If so says "it might be in Manhattan, hotel rooms are particularly expensive there, but it is not possible to give a definite answer", fine.
If someone starts bullshitting, not so good.
Another one at high-school level maths:
A room has one wall that is 16ft long, another one that is 24ft long. What is the area of the floor of the room?
It might be reasonable to assume a rectangular room, but it's not given. So it should be expected to give a nuanced answer.
Even more callous would be to say the room is rectangular and then point out that the floor might be tilted :D
But yeah, I would be pretty annoyed by that, too. I mean, nobody would say that it's a good answer to start fretting about curved space-time or something given this question.
But in every domain, I think it's possible to design good "trick questions".
The more I think about it, this type of question is basically the same type of question one would use to "benchmark" an LLM.
And again, I'm not saying that I'd answer these correctly...