Neither will I on a flight, and it has nothing to do with a dress code (although I've been a NRSA passenger exactly once in the past ten years).
In the admittedly remote possibility that you will have to get out fast--emergency evacuation--you do NOT want to go down a slide in shorts (rugburn!), and you want shoes that will stay on your feet and enable you to move away--fast--from any possible fire and/or explosion. That's my reason for my 'dress code'!