I am intrigued. Would you care to explain? The way I see it, you may be talking about apparent solar time, in which case high noon is defined as 12:00. Or you may be talking about local time, where the exact time of your local high noon depends on your relative position within the time zone and on daylight saving. Although a permanent daylight saving idea keeps popping up from time to time and has or had in fact been implemented in some countries, it is by no means common.

With the odd exception of countries using a single time zone despite spanning several time zones geographically, or using the "wrong" time zone, your local high noon is usually somewhere between 12 and 1 pm, thanks to most time zones' west bias. With daylight savings on, this changes to between 1 and 2 pm.

But my understanding may be wrong. I would like to know where your claim that is is exactly 13:00 throughout the year comes from. Maybe I am missing something obvious.