Our time syatem is not illogical and if you think it is you haven't thought about the consequences. The only bad thing about timezones is how far they swing away from their ideal position sometimes.
Sega used this in their pioneering MMO from ~1999, Phantasy Star Online. “Beat Time”. The idea was to help you coordinate meeting times with people regardless of time zone. The problem was we had to convert it to regular time to have any idea when 725 beats was or how long 150 beats from now was.
Honestly, all we need to do is eliminate time zones. It wouldn’t solve all the problems with time systems, particularly for programmers, but it would go a long way to solving the practical problems humans face, as well as eliminating one of the biggest machine problems.
Just everyone switch to UTC. As I write this it is 10:51 UTC. Anyone in the world can convert that to their local purpose. In eastern Australia, 10:51 is mid evening. In the UK it’s late morning. In western United States it’s late at night. If we always used UTC, people would just be used to this pretty quick.
We have UTC/GMT my dudes. Just count times by that and boom, no time zones. You can even remove a colon, meaning you just end up with 4 numbers, like 1700 for 17:00 UTC (5pm Greenwich time)
And we sat there, waiting for the other shoe to drop, crickets.
So how do you tell someone when your day starts? How do you coordinate multi content projects?
What's the minimum time segment? Just under 90 seconds. So no more microwaving for 30 seconds, or do we start with fractional beats?
I feel like trying to switch to this would cause more problems than it would solve. If you switch to this time system, what do you do about all the other units of measure that include a time component? Either everything has to change, or you have to start using two different time systems.
I don't know, way back in the internet 1.0 days.... my child brain hung out with some other kids of similar age on chat channels. Time zones fucking boggled my mind at the time, and I tried to sell some other people on this shit so we could always meet up at the same time to chat.
TL;DR - I "bought into" the marketting as a kid... I always did like watches, tried to convince some internet buddies to use the shit. Later in life, understood how timezones worked.