That is what Iceland did. Before the 1960's Iceland observed the daylight saving hour by switched from Iceland standard time (GMT-1) to GMT. In 1968 however, Iceland decided to stay on the daylight saving hour making true noon in Reykjavík often around 13:30.
Having grown in those hours I have to say it kind of sucks. You wake up in darkness most of the year. If you wake up at 7:00 local time, that means you wake up at 5:30 solar time.
There are loud voices (including psychologists and medical experts) that are advocating for moving Iceland back to Icelandic standard time (UTC-1). They claim the lack of sunshine can have detrimental effect on the sleeping cycle and therefor the general health of the population. Adding an extra hour of sun in the morning might be helpful for the general population.