For instance, we handle 24 hour clock (with 60 minute hours?! WTF?) fine, even if it's insane and we use the decimal system elsewhere. Because we got used to it when we grew up. Many even have the clock reset in the middle of the day, ending up with things like two hour activities spanning from eleven to one! (Don't get me started on shit like "half four" - it means different things depending on where you are, but it never means two!)
Heck, there's a whole, huge country that gets by on inches and ounces and pounds and miles and whatnot - a mind boggling amount of extra mental energy required, and with the exception of some recent lapse when selecting their boss dude they seem to be doing mostly as well as (and over the previous century arguably somewhat better than) the rest of us in the thinking department.
If we grew up with date/day changing in the afternoon, every kid in preschool would have it figured out already. "Early morning flight confusion" would seize to exist (except, perhaps, for the poor bastards who'd happen to live close to wherever we decided to place the prime meridian), because everybody would know what "1:20" meant, and not randomly guess at something based on when they happen to sleep.