Ask HN: Should interviewees start asking their own coding challenges?

During the interview process, it's often said that the interviewee is interviewing the company as much as the company is interviewing the interviewee. Therefore, it seems fair to ask the company engineers to solve a programming question to prove their competency in an area that is important to the interviewee. If this became standard practice, I believe that we could start to fix the broken technical interview process that plagues our industry.