I feel like it changes the meaning of “day”. In some contexts, day is the daylight hours… but in this context it is from when you woke up to when you went to sleep. So it feels a bit more timezone agnostic. But only a tiny bit. This would be more ture if you were comparing have a good afternoon to have a good day.

But the real answer. Someone just didn’t like saying the same thing over and over, so threw in some variation. Someone else who wanted to suck up to them started using it. Others just happened to follow.