I have never used Sketch, so I could be wrong here, but I think the reason that you can't remove this tail shape is because it is not created by having one shape laid on top of a separate shape, but is simply a complex path interacting with itself.
When you try to fix it using subtract and it seems to work strangely, it is because you end up subtracting all of the complex portion of your original path, and only retaining the section that overlaps with the new rectangular path.
The only way I know to fix this is to delete the individual points in your path that are causing this white triangle-the point at the very tip of the triangle and the one that is just on the border between the white and purple. Hopefully that is something you can do in Sketch.
As an aside, I frequently find that if I have a path/shape that is doing something that I just can't seem to fix, if I go into that path and remove an individual point or two, I suddenly have a better insight into how the path was constructed and how I can fix multiple problems that I am seeing with it.
By the way, I know you said that you already knew that you could solve it by removing the individual points, but we're looking for a different solution, and I didn't provide a different solution. That's because I don't think the program itself is necessarily able to "understand" what you want to accomplish. Maybe if you draw a path that covers the section you want to eliminate, and choose an "add" function, it might be successful, but I don't know that it would be less time consuming than simply deleting the stray points.