Pax Empyrean likes to think of Cinderella’s prince as a master strategist:
They had a ball and invited all the girls in the kingdom. This lets the prince see what all the girls look like when they’re dressed up and how well they conduct themselves at social functions, but that’s not actually all that important. What he needed, after determining whether a girl could pass muster as the public face of the monarchy, was an excuse to make a surprise visit to all of these girls to see what they look like when they’re not doing their best to dress up for him, because he’s a smart enough dude to know that makeup and fancy clothes are how women lie to you that they’re attractive when they really aren’t, and a monarch doesn’t stay in power for long without double checking everybody’s lies. The shoe is just an excuse to make these surprise visits. If that hadn’t happened, he’d have found something else.
(Hat tip to Borepatch.)