In an absolute scale, the probabilities of an accident at any one moment are very small. So, I think that it is typical that one can go through many intersections without incident in a carefree manner. But the relative risk of going through intersections is probably much higher than riding legally on a typical road between intersections.

My guess is that you (Laika) also have a considerable amount of experience riding among traffic such that a lot of actions that a new rider would have to do consciously, you are able to compute subconsciously.

Is the risk overstated? My interpretation is that you mean, "Is too much emphasis given to negotiating intersections when safety is discussed or taught to a new rider?" My feeling is no.