My birthday would always be on a Sunday!
There's also "Sun day"(Sunday), "Moon day"(Monday), "Fire day"(Tuesday), "Water day"(Wednesday), "Tree day"(Thursday), "Gold day"(Friday), "Earth day"(Saturday). So your claim is wrong in Japanese for every day except Sunday.
If you see something written like 四日("4 day"), this refers to the day of the month not the day of the week(for Japanese).
I remembered Japanese copied the Chinese at something there, but, whoops, it was the names of the planets that were copied. So the Chinese names of Mars(火星), Mercury(水星), Jupiter(木星), Venus(金星), and Saturn(土星) are copied onto the same days as planets that Romance languages name their days after.
My interpretation has always been that 日 is meant to represent "zero", but I never put any thought into why they didn't just call it 星期零.
I've noticed while living in China that, whereas Westerners like me virtually always remember what day of week it is but often forget the date in the month, Chinese are more likely to remember the day of the month and forget the day of the week.
Confusingly, the "seven luminaries" system in that article aren't just referencing the planets: they're also the names of Sun, Moon, Fire, Water, Wood, Metal, and Earth. I did get that sorted out by looking up Western alchemical ordering for the planets, which is in the same order. Wikipedia helpfully provides a table that includes the old names for the planets as well: