I think that question about why manhole covers are round is more of a urban legend than anything else. Or it might be a question asked to someone applying for a non-technical role, to see how they reason about the issue (though it is most definitely not the best question to achieve so).
I was asked that question during an interview for a technical role at Microsoft. Granted, it was 13 years ago at this point, but they did really ask stuff like that, and probably still do.
My impression is that they are no longer in vogue - for a few years when I was in college (2004-ish) they were all over the place. Our industry is extremely faddish, even when it comes to interviewing...
You can still see them in some places I believe. I've heard anecdotally that Microsoft is still a fan of them.
When I was trained as an interviewer at Microsoft (circa 2006), they explicitly warned people against asking questions like that (and had been doing so for some time). There may be older employees who stubbornly persist, though.
I should add that my personal experience contrasts with yours - I did a lot of interviews around 2004 and got asked riddle-type questions by one, maybe two, people. My memory is that they mostly died with the original dot-com boom.
Entirely an informational note, but the manhole-covers question actually originated at Microsoft if I recall correctly. There are several references to it around the web, and at least one primary source confirmation by an interviewer that he used the question on multiple occasions [1].
That said, the fact that it was first introduced by a highly successful company doesn't lend it any merit in my book.
Anecdotal, yes, but I have actually been asked the manhole cover question in an interview. Even if it started out as an urban legend, it does appear to be in use in the wild now.
The question never made any sense. Lots of manhole covers are rectangular. As long as the lip of the manhole is round and small enough, it still won't fall through.