Extremely frustrating experience in a system design intrview

So yesterday I did my final round of interviews with a company. I had a really hard time with the format of the system design interview. I was basically given a task to construct a survey builder whic

So yesterday I did my final round of interviews with a company. I had a really hard time with the format of the system design interview. I was basically given a task to construct a survey builder which asks questions from members in dynamic flexible ways in different critical parts of user's fitness journey. In my mind I gave an answer that I knew I could implement myself because I've done something like this before, but the interviewers gave negative feedback and I was rejected outright without completing. I was basically discussing my approach while making a diagram on a small whiteboard that I was holding, while erasing it to demo other parts of the system, create data structures, etc.. I was having a bit of a hard time conceptualizing the solution to this problem by doing it this way, I got lost a few times and paused. Looking back I wish I would have thought to load some diagramming program and sharing my screen. I'm wondering, is it normal for a system design interviewer to not give any kind of guidelines or provide a framework/sandbox to share information? It would have been really helpful. Was that step up to me? How does that usually work? I feel like I was rejected because of this technicality.