I think there are two answers: the bad answer is that people think of interviews as school finals, with all the same connotations about potential for cheating,

I think there are two answers: the bad answer is that people think of interviews as school finals, with all the same connotations about potential for cheating, cramming, memorization-without-retention, etc. The good answer (IMHO) is that the format allows the interviewer to evaluate how a candidate deals with prioritizing conflicts of interest (i.e. the desire to write clean code vs desire to just get something out due time constraints pressure). It also opens up opportunities to explore refactoring, whereas a primed candidate might just bang out "perfect" code the first time around, and not leave much room for evaluating their iterative process.