I've never had a problem with my pumps with the elastic at the front and no straps. However, I'll tell you a funny story:
I have a friend who's a professional competitor. At one comp, right as tango was starting, she somehow lost a shoe. And couldn't find it. (Yes, she was on the dance floor and LOST a shoe!) They had to get a move on, so she kicked off her other shoe and danced the tango in bare feet! She said it was the best dance she's ever had...at least it was tango and not foxtrot! :) Anyway, after the dance ended, they found the shoe...it was caught by the heel in her partner's cuff or shoe or something. :)