Making such discoveries depends on one's nature. A very good friend of mine for instance, hates surprises, by nature. The progress she makes in life is an outcome of careful planning. She enjoys life better that way. I have tried to show her several times that it is OK to do an unplanned activity. Once, she was wondering about how she can get back in shape in her busy life (which involved raising two kids). She spent quite some time thinking about it. And then one day, all of a sudden, I almost dragged her into a bike shop and we bought a bicycle for her. I said she could bike to work, do her farmers' market trips on the bike etc. And she did. It has been three years since that and she has only thanked me about this spontaneous act. It has helped her significantly (although biking on the streets of the Bay Area is not safe for someone like her, or anyone for that matter).
We have talked at length about this and other similar incidences and I think I now understand her plight. Leaving something to chance knowingly is something she just cannot do. Of course, like we make little adjustments to our nature, she could make some provision for accidental discoveries. But I now appreciate that it is hard for someone like her. Just like it is hard for someone like me to "plan the work and then work the plan".
She says, to an extent, making rich discoveries by being serendipitous is like a successful startup. For every successful startup, there are a bunch of failed ones. Thus, there should be many gaffes, stressful situations because you hoped to make a rich discovery by accident. And when you do make a rich discovery you tend to forget the pain you endured.
I am not sure if I can successfully refute her.
Another subtle observation I have about being serendipitous is that it suggests somewhat philosophical concept of destiny. A wise man (a physicist by profession) once told me that it is amazing how things that happen to us give an illusion that we make them happen. If you think about it, this is not something that you can quickly brush aside. When there are multiple choices available, what decides the choice we make?