It is a fraction of the lunar month…about 1/4.2. That’s hardly a nice clean division of the lunar month. You’d be a heck of a lot closer with 5 weeks of 6 days each!
In Rome, interest and rent were mostly computed by the month, and the days inserted to keep the calendar aligned were deliberately between years to make these calculations easy to do (no interest or rent was due, and they could not be used as start or stop days of contractual relationships).
Using a pencil influenced other modern things too, like the Dow indexes and GDP.
For a similar reason, it might have been better if humanity had settled on a base 12 number system rather than base 10. We can only easily halve 10 while we can easily halve, third, and quarter 12. More factors means it's more intuitive to reason about common fractions of things.
Earlier civilizations did use base 12, and we still have elements of that history in common use, like the special names for eleven and twelve in the English language and our 12 hour clocks. A common theory for the prevalence of myths about 6 fingered foreigners in the Bible is that these other cultures used base 12 numbers, and the only way people using base 10 could understand that was to assume that they must have 6 fingers to count with. Interestingly, you can actually use your fingers to count to 12, using the 3 segments on each of your 4 fingers rather than the 5 whole fingers.
Sure, but the nice 4 week period is not actually anywhere close to a lunar month, so the "groupings of 4 weeks" part makes sense because 4 is a nice number, but the "7 days to a week because 4 of them will add up to a lunar month" thing is just not even close. We're not talking about something like leap seconds where the drift is slow relative to a human lifespan. 28 days is a whole day and a half shorter than a lunar month.