Why in the first place?
Since this is such a rare occurrence and a second is so small, why do we do it? I have yet to hear any reasonable argument for. To get an offset of five minutes we need a millennium. So maybe people are a bit nostalgic (autistic) and need the time to be 12 when the sun is in the south. Guess what, it isn't. Daylight saving time offsets that by an hour, but alright lets look apart from that. The time zones are quite wide and usually expanding into the last one and the next one in some places, so you have up to half an hour offset there as well. But, let us assume you don't use daylight saving time and live exactly on a longitude divisible by 15 then sun still will be in the south at 12 only on four occurrences each year due astronomical time is not sundial time, but mean solar time and the offset called the equation of time is up to 16 minutes.
Can anybody enlighten me as to why we use leap seconds? It seems to me that for it to become an offset greater than what we experience throughout the year anyway we will have to wait over three thousand years. Isn't that something we could leave for that generation?