Meh, I am unconvinced.

It is 04:25 (“four twenty-five”) there, same as it is here. Does that mean I can call him? I don’t know.

Of course. But instead of asking “what time is it in $location” you just ask “what time do people wake up in $location”. Really quite simple. In fact it is way more simple because when you get 04:25 you don’t need to then say “Ok, I’ll call in 5h, what is that here. That is $time here”. Ok, I’ll let him know I’ll call at 09:25 local time and I’ll put it in my calendar at $time. Instead you just say “Ok, I’ll call at 9:25, I’ll let him know 9:25 and I’ll put 9:25 in my calendar”. And you automatically know that you will still be awake at 9:25 because you know what time you go to bed, you don’t need to convert it back to your time zone (or do the math again adding 5h to your current time) to check.

To address the summary:

causes the question “What time is it there?” to be useless/unanswerable

That is a feature. We can agree on what time it is! This is a huge benefit. No more time-zone conversion errors and people showing up to a meeting 1h apart because someone made a mistake.

necessitates significant changes to the way in which normal people talk about time convolutes timetables, where present means “days” are no longer the same as “days”

I agree. I think this is something that we will need to get used to and the biggest concern about not syncing “day” to the sleep cycle. But you know what?

• This is already a solved problem for 24h shift workers, they seem to figure it out quickly.
• This is already a problem when calling across timezones. You can’t have a “tuesday call” or talk again tomorrow.

It is hard to tell how a whole society will adjust, but I think it will be solved within a couple of years of minor confusion.

complicates both secular and religious law

This seems silly. I’m sure we will figure out how to add a “no trading on sunday” law if we want to.

is a staggering inconvenience for a minimum of five billion people

This is only true if we agree with your other points.

makes it near-impossible to reason about time in other parts of the world

What? how so?

does not mean everybody gets up at the same time, goes to work at the same time, or goes to bed at the same time

Of course it doesn’t, the sun is important and this would be silly.

is not simpler.

That is your opinion.