With its building block style, and being a new language, why did Esperanto use existing variations of days and months, instead of a neutral, generic, building block approach, for example using Unuamonato instead of January?
It has to be remembered that the months of the Gregorian calendar aren't universal.
In the West, the first month is January. In the Jewish calendar, the first month is Nisan; in Muslim countries, the first month is Muharram; the first month of the Hindu calendar is Chaitra. None of these coincide, and in fact Muharram can occur in any season. Thus, Januaro is essentially a technical term in the same way that Nisan is. Replacing it with unua monato would have to be done with great caution, especially in historical texts, as January was not always considered to be the start of the year.
East Asian languages use only numbers for the Gregorian months, but it was never their practice to give names to months, and the calendar was purely administrative. Conceivably, you could invent easier-to-remember names (Munu, Modu, Motri, or something like that) but that starts to resemble an attempt at calendar reform, which was never a part of the Esperanto project. (Zamenhof would have been well aware of previous attempts at simplifying the calendar.) You can always write 2016.9.16 and say du mil dek ses, punkt naŭ, punkt dek ses.
We already have a word for day tago. What if we could make a system there, the days of the week will all be first syllable ta plus a number 1-7 (starts at Monday) plus the last syllable go. This would make the days of the week to be as such: Taunugo, tadugo, tatrigo, takvargo, takvingo, tasesgo, tasepgo. Please notice that Esperanto, unlike English, do not write their days of the week with upper case. Wouldn't this be so much easier!