It seems like it would be a bit confusing, though, if you had to relearn times whenever you travel somewhere (edit: and dates could flip over in the middle of a work day). But maybe you’d prefer that.

I'd prefer that over having to change clocks when you travel, and having to have knowledge about the location and possibly having to flip the date when you encounter a reference to a specific time, yes.

Before they were invented, it was literally just anarchy. People set it to match people they knew. That’s what I was thinking of, but it could also just be one place where noon is at 12:00 PM.

Yes, you would obviously do the latter. No sense it going back to the bad old days.

Well, there’s not a round number of second in a day, or days in a year, for example, since they’re all naturally occurring and arbitrary.

Days in a year ok (except leap years). But seconds in a day are round (discounting days with leap seconds). 24 * 60 * 60 = 86400, which is divisible by two. Did you mean they are not based on the decimal system? I'd be up for a decimal based time system and a reorganised calendar, but that wasn't the topic of discussion here.

And then the Earth turns at a subtly non-constant rate, and people have settled on a seven day week.

Yeah but none of that has much impact on the timezone debate.

If you do have timezones, it doesn’t make sense to be inflexible with them when they run up against geography or trade and cultural ties, so they’ll be curvy, and geopolitics will itself change over decades and someone will want to change which one they’re in.

Fair enough. I acknowledged this point in my other post, that there are historical reasons for timezones mostly rooted in administrative requirements. But I don't think this is a good reason to not adopt a better system per se.

All of this is a headache if you just want to do a calendar calculation.

Exactly! So out with the old, in with the new. Sure this will create some other headaches, especially given how deeply rooted some of the relevant nomenclature is in most languages, but the sooner we change this the less it will hurt. I see that it might be a non-starter given the inertia and disunity of globalised society working against it, but it still seems desirable nonetheless, to me at least.