To provide a perspective from the other side of the table: I conducted a good share of job interviews for my company and would likely pose a comparable question to the applicant mostly to determine a) their ability to grasp a problem and to reflect on the degree of their understanding of it, b) test their behavior in situations that are over their head and c) test their ability to come up with and discuss solutions based on reasoning and the facts given.
For a) I would expect the applicant to identify what information is missing and either to communicate assumptions for the white spots on the map or to pose relevant questions. Regarding b), I would expect the applicant to openly state if they feel that the challenge is above their head _but_ try to give me a solution nonetheless. Which brings me to c): I would not expect a working solution; not even a complete one. I would like to see whether the applicant can work on given input and outline the reasoning behind the suggested solution in a coherent and understandable way based on that input.
My bottom line for you would be, that if you think what I said might apply to the interviews you experienced, you should try to re-frame such questions for yourself. Unless you see yourself unfit to adapt your approach (which I do not think, as ASKing-HN is proof for existent self-reflection), I see no reason in what you wrote that indicates that you should leave the industry.