You have wakened my curiosity here...

I had heard that of the ancient Greeks, though Wikipedia gives the origin more vaguely as the ancient Near East. It is a practical way of thinking when you are outdoors most of the time, you are not very active at night, and a sundial is your timekeeper. It also helps to be at a relatively low latitude, where the seasonal variation is not so great.

This makes sunrise and sunset the important moments in daily timekeeping, and this is, of course, the case in the Jewish definition of a day (I would not be surprised to learn that Jewish scholars also worked with intraday fractions of the lunar cycle.)

If this did lead to a willingness to vary the second along with the length of the hour, this would seem to me to argue against the specialness of the definition of the second as 1/86400 of the mean synodic day. I doubt, however, that anyone but perhaps a few scholars at that time ever contemplated such a small division of time. The second only became a practical measure with the development of accurate mechanical clocks, by by then, mean time had largely taken over sundials and other forms of intraday ephemeris timekeeping, as that is what mechanical clocks measure. (This transition, I suspect, had a greater impact on the general population than did the adoption of the atomic standard, if only because the latter had no practical impact.) At that point, the second was defined by sexagisimal division of the hour (and thus, obviously, transitively as a fraction of a particular mean synodic day, given the definition of an hour in such terms.)

https://en.wikipedia.org/wiki/Hour https://en.wikipedia.org/wiki/Second#History_of_definition

You can't deny the implication, but whether that elevates it to a position of special relevance is another matter, at least as I see it. Personally, unless I have been thinking about it recently (which is very rarely), I would have to do the calculation before answering the question of how many seconds are in a day (and if I were being more than usually pedantic, I would have to ask "which day?")

In my view (which, admittedly, is somewhat subjective), people are not even tacitly concerned with the number of seconds in a day unless they are contemplating the number of seconds in an approximately day-length or longer period. On the other hand, I can imagine some of my relatives, who were conservative in all matters almost by reflex, responding to the SI definition by saying something like "Nonsense! there are sixty seconds in a minute, sixty minutes in an hour, and twenty-four hours in a day, and that's that!" - once they had learned something, it was set in stone. I am pretty sure that the annual variability of the synodic day was not among the things they had learned, and the idea of a leap second would be deeply troubling.

I appear to have talked myself into agreeing with you that 60.60.24 is what matters to most people by default, as they don't know the minutiae of celestial timekeeping or the increasing importance of atomic timekeeping (let alone relativity!) in their everyday lives.