The question isn't whether you should reinvent the wheel, it's whether you can if need be. It is important for companies to weed out candidates that can talk a good game but are useless when it comes to actual programming. So maybe in the process good candidates fall through the cracks, but then again, nobody has invented a perfect way to interview candidates.

In any case, how would you even go about knowing whether a certain piece of existing code that you blindly pulled in from some random place is optimized for your particular use case without first being able to conceptually understand it - which is all an interview is. Nobody expects candidates to create production ready code on a whiteboard.