The questions are more a means of judging whether you're nervous or behaving suspiciously. The actual answers are irrelevant unless they're especially bizarre.
Nerves are not a measure of someone's guilt of anything. Life is a bit more complicated than that. Im sure we are aware of many world leaders who lie quite confidently and your trap would never catch them.
It's not used to establish guilt, but to establish whether the person is worth further examination, so false positives (e.g. due to language difficulties) would just lead to either further interviewing or searching.
There's not really any good reason to not do it as the questions are not overly intrusive.
Firstly the staff would need training to effectively ask the right questions and interpret the responses.
Asking the public questions cost time. If you have two lines and one does the required checks and the other also asks questions and conversations happen, the later will be slower.
Slower lines means more staff are required.
The questions are usually asked at the same time as passport checks are performed so I doubt it takes much longer at all.