Noon is generally not midday for most people. Far more stores are open at 7 PM than are open at 5 AM. Far more people are still up at 9 PM than are waking up at 3 AM. And the "9 to 5" song would center the day at 1 PM. It seems that in general society has decided hours after 12 PM are more useful than hours before 12 PM. It's far easier to just change the clocks to have 1 PM be midday, keeping DST year round, than to change society.