There is a very good reason cyclists are not allowed to cross at pedestrian crossings unless unmounted. Bicycles approach at a much higher rate of speed then pedestrians. When you are making a right turn, there are a LOT of things to watch for, when you have checked to ensure no pedestrians, you need to check for traffic turning left from the opposite side, when a bike pops out of nowhere, one cannot be expected to see it. It is really that simple. I think certain things need be explained to some people who do not drive. A driver can only look at one direction at a time, and if you place yourself somewhere you are not expected to be, you MAY DIE.