1 lunar month = 29.53059 days
1 lunar phase (1st quarter, full moon, third quarter, new moon) = 29.5305 / 4 = 7.3826 days
Yes, that works to a certain degree. IMHO, good point.
Every lunar month would have at least one eight day week (which reminds me of a song from Paul McCartney and the Beatles ). The lunar month is one explanation for the seven day week (if you prefer to omit the other cited explanation).
For multiple reasons, I like the consistent Design of the 7 day week happening every week. It makes work weeks and scheduling to be easier.