[drostie]

You're not going to convince either the Christians or the Jews to do a week that isn't 7 days long. That number is more or less fixed by the sizeable minority who need it for the rest of their habits.

The solar year is convenient so that one can speak of "the average historical weather for this month" and such... but it's true that many others have done lunar calendars etc.

[hasenj]

Muslims use the lunar calendar for religious occasions (Ramada, Hajj, Eid) but use the Christian, solar calendar (like the rest of the world) for everyday life.

[vorg]

The day and year are settled astronomically. As for the week, it's been in use for at least 2500 years continuously without ever skipping a day and now virtually every country uses it. The month, however, has variable length, has been redefined every thousand years or so, and has competing systems from Islam, Hindu, Jewish, Japanese and other cultures. The month can change, but the week never can.

[mark-r]

That makes the extra day that isn't part of a week kind of problematic, doesn't it?