Nothing "makes sense" about an arbitrary number. That's why it's arbitrary. It makes an equal amount of sense to say that mean local solar noon is 183615.
The system we have doesn't work because the problem is how to coordinate billions of humans. No solution will ever work, because you can't perfectly coordinate any number of humans greater than about 500. The mess we have now is just built upon centuries of kludges, each trying to improve on how civil time was defined beforehand.
Why are there 24 principal time zones? Because the clock has 24 hours. Why does the clock have 24 hours, with 60 minutes each? Because Sumerians counted on their fingerbones, and Babylonians liked base-60.
Machines, on the other hand, can coordinate perfectly fine on the number of milliseconds since 1Jan1970, at the center of the main telescope of the original Greenwich Observatory. The zone file is the only thing holding the stupid mess together. We could specify civil time to be any rule-based system whatsoever, and the computer clock would still allow us to coordinate with the rest of the world.
With the invention of cheap ubiquitous computing and piezocrystal-mediated clocks, it makes sense to throw out every unit other than the SI second, and stop trying to coordinate things that don't need to be coordinated. Schoolkids don't need to be in their homeroom seats at the same time the NYSE opens. The fast food chain stores don't all need to stop serving breakfast at exactly the same time. And companies don't need to have the same business hours as the local bank branch.
Most owls, as opposed to most larks, would rather get up after sunrise, rather than before it. Tired (literally) of larks setting the schedule for everyone just because they wake up first.
