Lots of folks do it. On of the gyms where I taught actually didn't have clipless pedals. I HATED IT and brough in my own pedals.
Here are a couple of observations from me:
No matter how tight you tighten the toe cage, you still probably can't utilize/strengthen your hamstrings glutes as much as you can with clipless pedals.
Most running shoes have a very soft sole -- not optimal for cycling (power transfer) and some folks experience burning/discomfort in the soles of their feet from the soft sole.
If you participate in classes where you stand frequently, you may experience some pain in your toes or balls of your feet.
Most toe cages are pretty one-size-fits-most. This means that you might not achieve optimal positioning of your foot on the pedal (or your knee over the pedal spindle).