The Earth Epic Calendar has seven-day weeks because that is what just about the entire world uses.
People may opt to use the traditional names of the days of the week on the Earth Epic Calendar. I have also introduced names of the days of the week that are more secular. Few people know this, but the days Tuesday through Friday are named after Norse pagan gods, and Saturday is named after Saturn, a Greek pagan god. There is, of course, nothing wrong with that, but some people may prefer more secular or religion-neutral expressions of the days of the week. (The Quakers simply number the days of the week from one through seven.) Therefore the Earth Epic Calendar offers this as an option.
The days are named as follows:
Starting all quarters on the same day of the week–almost
Many calendar reformers combined quarters with a leap day or two not assigned to any day of the week in order to have a perpetual calendar in which the quarter starts on the same day of the week every quarter., every year (It would presumably start on a Sunday). The months within quarters would have started on different days, but would still have a consistent pattern. In the proposed World Calendar, January, April, July and October would always have started on a Sunday, February, May, August, and November would have always started on a Wednesday, and March, June, September and December would have always started on a Friday.
But as I mentioned before, the World Calendar reforms were never adopted in part due to objection from people who felt that requirement to honor the sabbath every seven days would put them in the awkward position of having a different sabbath day every year.
With the Abrahamic religions being so dominant in the world today, its probably more practical to simply accomodate their needs for an every seventh-day sabbat. But still, in most years, the first three Quarters in the Earth Epic Calendar start on the same day of the month, and the fourth quarter starts on the day of the week after the previous three quarters. Thus, the third quarter, Northlight, has a 92nd day, so then the final quarter, Westlight would start one day of the week later than it did at Northlight. In leap years (such as 11721), Eastlight has a 92nd day, so in those cases, the first day of Northlight will be one week day forward and then the first day of Westlight will be one more day of the week forward because it has one more day forward.. That’s still much easier to track than the first days of the month, which jump back and forth between the days of the week.
The future of the week
It will be up to future generations to decide whether to continue with a seven-day week. The seven-day week is not inherently critical to the structure of the Earth Epic Calendar.
Instead of seven day weeks, one option would be to divide the quarter into roughly nine units of ten days each. As such, it would not be necessary to even have named days of the week, as the last digit of the date would be sufficient to determine the day of the week. This was tried during the French Revolution, but was unpopular largely due to laborers only getting 1 1/2 days of rest out of 10. The current five day work week means that 28.5% of the week is set aside for rest (though, unfortunately, many workplaces require six and even seven days of work per week.) A strong argument could be made for having three or even four out of the ten days being set aside for rest and recreation. But this is for society to decide for itself in the future.