Re: Let it slide
You're proving that you don't understand what time is for.
"We might as well get rid of leap days too. Yes, this will make the new year slide more quickly from the winter solstice, but why should this matter? It's not like people sow and harvest according to the calendar any more."
Because "A January day in Australia" means something about the likely weather these days, but if we let January slide around the year, it stops meaning that thing. We use seasons, and having to look at season tables to figure out what was summer a couple decades ago will make things like predictions about weather and proper categorization of that data harder. And by the way, people do plant by the calendar as much as they once did and more in some cases. They always made adjustments for local conditions to optimize the harvest, but the general time of year is still used very often when deciding when to plant, and the main change is increased use of predicted weather which I've already pointed out relies on a calendar that matches the sun, because the sun is the primary determiner of our climate.
"Time zones are now oddly shaped and some even differ only by 30 minutes from the neighbouring zones (and there are more than 24 zones)."
Yes, and those could be solved best by making them better match geography. You'll get no argument from me about that and if you ever control the world, I'm happy to give you 24 nicely-sized ones respecting borders and we can reserve a punishment for the guy who decided that China (which needs three time zones) would only use one and it wouldn't even be the middle one.
"We could get rid of this complexity by using TAI globally (without offsets). So what if school starts at 14:00 some places on earth and at 04:00 in other places?"
Midnight is the problem. The people around the prime meridian get to be asleep while days change, but everyone else gets the days switching while they're working. If you live in eastern Australia and the days switch at what would have been 10:00, do you stop working in mid morning when Friday ends? It also means that you can describe a time and everyone knows what that means in relation to the day without having to ask you where you were at the time.
"Let us have twelve 30-day months per year, even if this slides by 5.256 days relative to solstice every year."
Ah, so you're looking for months to slide around the solar year every five decades, reversing seasons from summer to winter three or four times in a lifetime. If I ever get to assign people to fix the time system, I'm afraid you're ineligible to work on calendars.