So you want to reform the week, the only time cycle that hasn't been altered in millennia to sync it with... what exactly?
Different groups of time have different goals. Scientific and technical applications only use the second. Years are useful both for agriculture and astronomy. Year subdivisions, weeks and months are useful for legal, social and personal purposes: weekends, holidays, celebrations, birthdays, embarrassing familiar reunions and all that.
They neither have to be in sync with anything, just being useful to track days in a year, nor they need to be mathematically pleasant, any programmers worth their salt will write you a perpetual calendar generator in five minutes.
No. I don't want to change the week at all. I'm just saying that "the week is 7 days so it's a quarter month" is broken as hell.
If you want a quarter month then have a quarter month.
Having a set of days that pretends to be a quarter month but rapidly falls out of sync is worse than having no quarter month at all.
If you gave any other reason for seven days, I wouldn't say it doesn't work right. But that reason makes the length of the week supremely half-assed.
> But it seems they didn't bother to change the names of previous layers. If something works, just leave it alone. You may argue that there are more "rational" ways to organize time measurement. I would recommend to read what Asimov had to say on the subject.
You're conflating two very different problems when you talk about it like that. Trying to make the units line up is legitimately difficult. Bad naming is not because of legitimate difficulty.