Note that the Sun position is not consistent throught the year and varies widely based on your latitude.

Good call. The definitions of "noon" and "midnight" would need to be formalized a bit more, but given any line of longitude, the sun passes directly over that line of longitude "exactly" once every 24 hours. (I put "exactly" in quotes because even that isn't quite exactly true, but we account for that kind of thing with leap seconds.) So you could base noon on something like "when the sun is directly over a point on such longitudinal line (and then round to the nearest hour)."

Could still be a little weird near the poles, but I think that definition would still be sensical. If you're way up north, for instance, and you're in the summer period when the sun never sets, you still just figure out your longitude and figure when the sun passes directly over some point on that longitudinal line.

Though in practice, I'd suspect the area right around the poles would pretty much just need to just decide on something and go with it so they don't end up having to do calculations to figure out whether it's "afternoon" or "morning" every time they move a few feet. Heh. (Not that a lot of folks spend a lot of time that close to the poles.) Maybe they'd just decide arbitrarily that the current day of the week and period of the day are whatever they currently are in Greenwich. Or maybe even abandon the use og day of the week and period of the day all together.

Just the days of the week? you mean that 2024-06-30 23:59 and 2024-07-01 00:01 can both be the same weekday and at the same time be different days? Would the definition of "day" be different based on whether you are talking about "day of the week" vs "universal day"?

Yup.

I'm just thinking about things like scheduling dentist appointments at my local dentist. I'd think it would be less confusing for ordinary local interactions like that if we could say "next Wednesday at 20:00" rather than having to keep track of the fact that depending what period of the day it is (relative to landmarks like "dinner time" or "midmorning") it may be a different day of the week.

And it's not like there aren't awkward mismatches beteen days of the week and days of the month now. Months don't always start on the first day of the week, for instance. (Hell. We don't even agree on what the first day of the week is.) "Weeks" are an artifact of lunar calendars. (And, to be fair, so are months.)

(And while we're on the topic of months, we should have 13 of 'em. 12 of length 30 each and one at the end of 5 days or on leap years 6 days. And they should be called "first month", "second month", "third month", etc. None of this "for weird historical reasons, October is the 10th month, even though the prefix 'oct' would seem to indicate it should be the 8th" bs. Lol.)