that just moves the weird math, because 11:00 + 1h = 00:00... The fact that clocks are a circle means there is some weird math like this happening somewhere no matter the system.
Not really 11:00 AM +1h becomes 00:00 PM, and vice versa. PM and AM are different prefixes/systems/units. Much simpler to understand IMO. 12:00 AM and 12:00 PM would no longer exist, you just convert them from PM to AM or back when you reach them and set the numbers to 00 again.