Yes, you still have to deal with timezones, but I'd much rather be given a UNIX timestamp for a UTC time and then adjust accordingly, rather than deal with all the other problems that come from communicating and converting between various other calendar formats and locales.
And this exchange should occur at the very last step, only when being displayed to the user. For almost any other purposes, there's no reason that two different applications should need to talk to each other using anything but UNIX timestamps. The potentially error-prone conversion should happen in the latest stage possible, because that's the part with the most knowledge of how any error should be corrected.
> At the same time, the human brain doesn't seem particularly well-suited to breaking down Unix time into meaningful scales,
But we're talking about for programming purposes - to a computer, one 64-bit int is as good as any other.