Same sort of question would be: "Why wear a tie at work?"
I think it's all down to etiquette and the message of respect towards each other that we feel is in "looking good", whatever looking good is according to the latest fashion.
Also a wrinkled piece of clothing doesn’t feel as nice as an ironed one, :-))
The experience of luxury?
Mind you, wearing ironed clothing in the old days was an ever greater sign of wealth and power.