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.