I used to use pedals with toe straps back in the day. I found I had to use a shoe made for cycling or the bottoms of my feet would be hurting by the end of the day. Cycling specific shoes have stiffer soles so the feet don't notice the pressure of the pedals as much. I'd assume a non-cycling shoe with the right sole might do the same.

When riding for three or less hours, a non-cycling shoe was fine.