I shot in program a few times, felt like I was on auto-pilot and with no creative control, and haven't touched it ever again.
TBH, if you're worried about missing a shot, it's not a question of using program mode or not. It's a question of keeping a very close watch on your environment, and predicting how things will develop before they do. If you anticipate enough, you can even have time to switch lenses.
On film this was a necessity, especially for candids. It had quite a lot to do with walking around with stops that were probably close to the right exposure in current lighting conditions, and guessing focal length and distance to the subject. Expose one shot right away if something develops, then get the correct settings and expose again and again.
Now toss in all the wonderful digital modes. You should still be anticipating, still planning ahead, but now the camera can give you the right exposure without you thinking about it. However, as a matter of personal preference, I know that in most cases I will want to be around f/4 (sadly my lenses aren't super-high-quality, so they both stop down to f/5.6 zoomed-in), to give me a good chance at catching movement in focus. So I set my camera on Av and let it handle the exposure. If I have time, I quickly check the histogram, adjust exposure comp, and continue shooting.