Yes, your foot can slip off a pedal, and yes, it can cause crashes. It even happens with clipless pedals when someone comes out of their pedal. But that mostly occurs during sprint efforts, not regular riding. So, if you're just doing rides and not contesting any big sprints, you have little to worry about.
Really thought, I think the bigger danger of flats is if your foot slips off while back pedaling/coasting and the pedal comes around smacks into your shin - I still have a divot in my right shin from that happening decades ago.