Yes, it's arbitrary, but we're on a continuum somewhere between every couple feet the time changes a few minutes and no adjustment at all and it feels to me like we're close to a happy medium.

It's not quite that simple. Timezones change (less often than postal codes, but across the world, it's still a bunch of maintenance changes). Getting rid of timezones would be simpler and reduce a monumental number of bugs (as well as code and potential problems). See the Russian changes!

https://www.timeanddate.com/news/time/

Only a few people have to maintain the time zone system, and only a few people (those writing the software that everybody else uses) have to understand the minutiae. The alternative is that everybody has to understand, which will invariably cause many mistakes.

I mean, when someone schedules an across-timezones meeting they use software anyway; and who really cares about that one time 2 decades ago when some small region switched timezones or whatever? (yes, I'm painfully aware that there are changes to timezones across the world pretty much every month; what I'm saying is how often does anyone really care about the historical changes, in contexts where the hour or 30 minutes really matters?)

Medical software certainly does. I imagine financial software as well.

Sure, but there it's on the programmer. Which is exactly what I mean - it's better to shift the onus to the few than having everybody needing to care about it.

OK, sure, but so what? The fact that it takes effort to maintain doesn't mean it isn't worth doing.