Yes, solar time matters as your biological rhythm depends on it. The most important part of it being able to have daylight when you either rise in the morning or at least have the sun get up quickly after that. Another important point is, that there is plenty of experimental evidence that shows that starting schools before the pupils are really awake is not effective.

It is a misconception, that "noon" is the middle point of your awake time. That was never the case. Our day usage most of the time is asymmetric: start the day and especially the work with the sunlight, spend the evening time off after work after sun set.

Using the high point of the sun as the reference for the daytime is a very practical choice, as this is the one easily observable time point which doesn't move much over the course of the year (a few minutes, but that is symmetric).