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).

IT matters when you have an economic zone in which some have 9am being 'basically mid-day', while the others have '9am being 'oh, the sun just went up'.

This traditionally has been solved in two ways:

1. do the split and accept that you will have costs associated with different time zones and sleep/wake cycles in your population (e.g.: USA / Soviet Russia)

2. don't do the split, and have the cost by putting a time/light adjustment burden on the population (e.g.: PRC, European Union)

My preferred solution would be to abandon all time zones and use something like UTC, or yet better: .beat / Biel Mean Time [1], which does not come with a 'oh, 12 means midday' penalty.

[1] https://en.wikipedia.org/wiki/Swatch_Internet_Time