Time up to days isn’t even that bad - it’s just base 60 because we get that part from ancient Mesopotamians who liked base 60 for the same reasons people like 12 (but maybe went a little overboard?). Since 12 is a factor of 60, going to base 12 would make hours-minutes-seconds jive better with other numbers. Only changing to base 12, a half day would be written as 10 hours, full day 20 hours. An hour as 50 minutes. A minute as 50 seconds.
I think there’s no helping higher than that - there’s no relation between months and days or months and years - they’re separate cycles that we just smushed together one day and refuse to separate. And days and years aren’t related in a convenient integer. Some things would coincidentally work out - 2 years could be written as 20 months - but for the most part there’s no way to line it up nicely.