Can you imagine hiring a surgeon, or a civil engineer, or, hell, a mechanic or carpenter based on brain-teaser questions? Nope. The interviewee would look at you like you'd grown an extra head, and probably start trying to figure out a way to bring the interview to an early end.
As such, they have nothing to do with reasoning ability. The "correct" answer is often completely wrong, like the claim that access hole covers are round "so they don't fall in", which misses the important point entirely. A circle is the minimum size cover that can't be dropped into the hole it covers. Make the cover twice as big as the hole and you have no problem. It is only under the common but special case of resource constraints that round covers are compelling.
There was also that ridiculous one about "how do you put an elephant in a refrigerator" where the "correct" answer depended on not knowing the difference between the definite and indefinite articles. The next question was "How do you put a giraffe in a refrigerator" and the "correct" answer was "You open the refrigerator, take out the elephant, and put in the giraffe". No one who was actually conversant with English could pass the test.
Don't tell me someone has used that as an interview question? That's a silly kids joke, after which you'd laugh childishly. There even was a follow up question, if an elephant and a giraffe would race, who'd win to give the other guy a chance to redeem himself.
The joke works a lot better with languages without definite and indefinite versions of nouns, like Finnish, and you mess up the joke with english where using the definite preposition would ruin the joke, and the indefinite form is not honest.
There is in fact a class of shapes that have the property that they can't fall into the hole which they cover (presuming a lip).
In addition to the above reason about it being the most efficient way to cover a hole, a round cover is also easy to move if heavy (you can roll it), very useful for something that likely has to be sturdy but also move-able.
Those measures were better than nothing, but not better than a good measure.
Edit, because I want to amplify on this a bit.
In the absence of any other measure, I'm willing to believe that someone who's good at brain teasers is somewhat more likely to be a good programmer than someone who isn't (though the correlation isn't going to be perfect, by any means).
The thing is that I can also believe that someone who's good at brain teasers is more likely to be a good surgeon or mechanic than someone who isn't.
Yet we don't use this type of question when we're interviewing surgeons or mechanics. Why not?
Edit: I don't mean to suggest that I think these kinds of questions are good for hiring software engineers, just that your argument for why that isn't the case may have some holes in it.