I don’t think the point is being able to use a specific language or to know a specific algorithm, unless the role requires it. If the goal is to test a person’s knowledge and understanding, then the actual implementation is probably less important than their ability to explain and reason about the problem. OTOH, if the goal is to find out whether the person is highly skilled in a specific language and has a lot of experience with an algorithmic domain, then what you’re asking isn’t unreasonable.

I think if it this way (very simplified): there are candidates that like challenges and who don't mind imperfect interviewing situations, and i had my fair share of people who dislike it would fare better if we just let them work on a real world problem. We did both for each candidate for some time, but the latter was much more costly and didn't provide such a good signal in the end.

Open-mindedness goes a long way. Also typically our interview questions are set up in a way where it's expected you won't finish but try, which reveals a lot about personality and how problems are attacked.