Time-weighted average has always seemed like such an odd name to me. I assume that taking a simple average of irregularly spaced points is a very common mistak

Time-weighted average has always seemed like such an odd name to me. I assume that taking a simple average of irregularly spaced points is a very common mistake and so that is likely where this name comes from. But, as another commenter pointed out, it really is just the mean value of a function.