That is where the burden is placed, but it doesn't change natural human limits. Bikes are small, silent, agile, and often erratic things that often ride within mere inches of a car (if they're weaving in between lanes). In a busy city, you can check the bike lane before you right turn, and a bike could easily slip back into it while you change your focus back to the intersection. I'm a pedestrian in a crowded city, so I know that drivers aren't always attentive and that's a big part of the problem, but I also drive on occasion, and it can be hard to stay on top of all of the cars, bikes, and pedestrians all around you (and many cyclists and pedestrians pay no regard to traffic laws).

so go at a speed that lets you stop before hitting anything you don't see. Why aren't drivers taught this?

This was part of my driver's education curriculum.