I mean, days of the year is fine as is because that matches seasonal cycles which is important for agriculture and the like. Ofcourse along the equator lunar calenders were historically used because they don't have different seasons but a calender used by everyone keeps things consistent for trade and the agricultural trade is still one of the most important things for humanity so it best remains a solar calendar.

As for time, 60 and 24 and in general multiples of 12 are great units because they can be easily divisible in many ways. This is why they were established as such in the first place, because Babylon had a big thing for what is called "extremely composite numbers" which are basically just a number that has more factors than any previous and equal to all subsequent ones (until the next extremely composite number) and all multiples of 12 (as far as I know) fall into this category. This means that units that are multiples of 12 both easily divide into each other (making it useful for changing between units) and easily divide into many other numbers making it easier to schedule a day as you have nice clean boundaries.