The main reason is because we use natural cycles that are important for civic and agricultural reasons as the basis of our measurements. And those cycles are unrelated phenomena that don’t match with each other well.

Day and year are based (duh) on two solar cycles (Earth’s rotation and translation), while the month and week are based on the lunar cycle of translation around the earth in roughly 28 days. When people tried to force lunar and solar calendars to fit, we ended up with the inconsistent months we have.

The 12/60 base divisions of the day were chosen before we had good calculators. Numbers with many divisors like 12 and 60 help a lot with mental math when you don’t have calculators.

There have been proposals of better calendars. The French tried something during the revolution and other people as well. The French republican calendar was:

• 1 hour = 100 minutes
• 1 day = 10 hours
• 1 week = 10 days
• 1 month = 3 weeks
• 1 year = 12 months + 5 monthless holiday

Another idea is the Cotsworth Plan:

• 1 minute = 100 seconds
• 1 hour = 100 minutes
• 1 day = 10 hours
• 1 week = 7 days
• 1 month = 4 weeks
• 1 year = 13 months + 1 special monthless holiday

I like the French Republican Calendar, but I would change it to months with 6 weeks of 5 days instead. And divide the week into 3 work days, 2 weekends. But the Cotsworth Plan is a better compromise between lunar and solar cycles.

Neither are good decimal systems. But in the end, if we want to use both the year and the day we’re fucked. There’s no way of having a fully decimal system. The year is approximately 365.25 days, and 365 is an awkward number. It’s only divisible by 5 and 73, so it’s not possible to have good divisions of it that match adequately a 10 based grid. You could abolish months and just have 73 weeks of 5 days, but I see no advantage.

We could do away with the year and just keep the day. We could do something like

• 1 miliday= 1000 microdays (1 microday ≈ 0.086 seconds)
• 1 deciday = 100 milidays (1 miliday ≈ 1.4 minutes)
• 1 day = 10 decidays (1 deciday = 2.4 hours)
• 1 decaday = 10 days (1 decaday ≈ 1.4 weeks)
• 1 hectoday = 10 decadays (1 hectoday ≈ 3.3 months)
• 1 kiloday = 10 hectodays (1 kiloday ≈ 2.74 years)

But this system would be totally misaligned with seasons, moon phases, solar cycles, etc. One could argue that those things are not as important for everyday life as they used to be, and that’s true. But they’re still economically important and you’d have to implement special calendars to keep track of them. It seems something like the Cotsworth or French systems make more economic sense.