I get the sarcasm, but given there are hundreds of millions of US border crossings annually, a policy of taking everything seriously regardless of size probably does make the US safer.
I'm sure that there are lines somewhere between 'taking things seriously', 'overreacting' and 'making examples of people'. Ask a stupid question, expect a stupid answer. It's a stupid question because nobody in their right mind would answer 'yes' to the question which just leaves people with a language barrier (which have a high incidence rate at borders), people that are nervous and/or tired (ditto, probably including some of the guards) and people that are trying to relieve the situation by attempting to be funny (stupid, but understandable since humor has been since time immemorial a natural release for tension).
I don't think it's necessarily a stupid question, because of the psychology involved with lying.
This question would likely weed out any wanna-be small time people intent on causing harm to the US. Something similar to how many criminals in the US are arrested due to routine traffic stops.
If asking this "stupid" question prevents 1 single undesirable person from entering the US, then it's served it's purpose.
You're completely right. There are serious downsides.
However, I think this question (and a lot of the crappy things about the US) exist to deal with and automate problems at scale. Scaling is hard. Scaling solutions are overkill if you don't have a scaling problem.
In this case, the problem is strong due process protections and allocating court resources. You might not hold a person without involving the courts if you suspect them of terrorist ties, but you can if they lie on a form or tell you they're a terrorist.
I don't know the specifics, but one could imagine a concession of due process if, say, the person held for their answer on the entry card is guaranteed to appear before a judge within three days.
Automate the process and you get silly situations like the one above. Don't automate the process and somebody eventually screws up and denies due process or lets a suspected terrorist through without scrutiny.
And again, yeah, the entry questions could be handled better, but it's a serious juggling act scaling it up and fitting it into our legal framework.