I’m quite confused as to how you’re actually proposing the time should work. I assume that when we talk about abolishing timezones, we mean that everyone switches to a single standard timezone (and that it still goes from 00:00 - 23:59). Are you saying that you would like:
a) The date-rollover point to happen at local solar midnight (i.e. 12 hours past when the sun is highest in the sky in your location, or roughly that), regardless of what the time actually is
b) The date-rollover point to happen at 00:00 standard time, but most people still wake up and go to sleep roughly around when the sun rises and sets
c) The date-rollover point to happen at 00:00 standard time, but most people wake up at roughly 07:00 (for the sake of argument, it could just be any standard time) and go to sleep roughly 22:00, regardless of where the sun is at those times
d) Some other scenario that I didn’t think of?
Maybe I suck at reading comprehension but I can’t tell which system you’re advocating for. I’m also confused when you give the example “15:00 on the 7th literally isn’t a time that can exist”, because however your system works, surely if 15:00 on the 8th is a time that you can refer to, then 15:00 on the 7th is just the time 24 hours before that? (I’m actually just very confused by your scenario. Are you referring to noon as the local solar noon, i.e. when the sun is highest in the sky, or are you referring to when the clock reads 12:00? In both cases I can’t figure out a way to make “15:00 on the 7th” impossible.)
Also I don’t think that the sunrise/sunset times being different throughout the year or that DST exists are indications that the solar cycle is independent of the date. Even if the sunrise/sunset happens at different times of the year, timezones are clearly meant to roughly center the waking day either side of 12:00 on the clock around the solar noon. DST exists to make sure that people get more sun during the afternoon when people are more active, so that both contribute to that the date-rollover point happens when it’s dark out and people are less active.