The reinterpretations of the Solstice celebrations to fit in various religions and the shift in the calendar from the true astronomical event have occurred much later.
By the time of Julius Cesar, after his calendar reform, the Winter Solstice occurred on the 25th of December, which is the reason for having Christmas on this day. The reason why Christmas is now shifted by 3 days from the solstice is that the Gregorian calendar reform has not restored the calendar of the time corresponding to the start of the Christian era, but the calendar of the 4th century (when the procedure for selecting the date for Easter has been established), and the calendar of the 4th century was shifted by these 3 days.
Before Julius Cesar, the Roman calendar shifted a lot from year to year in comparison with the astronomical calendar. It is likely that when first established, the 1st of March (their New Year) of the Roman calendar occurred on the Spring Equinox, but then it has drifted a lot. After the Julian calendar reform, the solstices and equinoxes occurred around the 25th of their months, then they have drifted away until the Gregorian reform has set them around the 22th of their months.
I expect this not to be true... Cultures with only a moon calendar (ancient Arabs) do not even have the means to express the date!
I doubt there was ~ever any society that couldn't tell you approximately where they were in the year anyway. All it takes is making marks on literally anything, one per day, or having a decent memory. What society doesn't have at least one person doing that?
You need seasons. Some places have very little seasonality. They tend to have a pure moon calendar.
I also doubt it was ever purely astronomical. Holidays would have happened because a lot of normal activity would have slowed or stopped in pre-industrial societies, and celebrations would have depended on what their traditions and beliefs about the significance of the solstice was.
The reason why normal activity slowed down around this time is astronomical. In Stockholm today, daylight started at around 9 in the morning and it was dark before 3 in the afternoon. Of every 24 hours, more than 18 are spent in darkness. Even daylight hours come with an asterisk: usually it's just a slightly less dark version of the night, because daytime rarely means sunshine. Stockholm sees less than an hour of sunshine per day in December, mostly clumped together on a few sunny days that you can easily miss if you're busy indoors.
The rich baggage of folk traditions and mythology is also deeply related to the shortest/longest days of the year - rebirth of the Sun, victory of light over darkness, etc are clearly of astronomical origins, with folk stories adding a layer of mystique to stimulate imagination and make things more interesting.
Midsummer, on the other side of the year, forms a pair with winter solstice, and is as big holiday as Christmas. In rural communities, Midsummer marked a brief pause between planting and harvesting. In modern times, Midsummer marks the start of summer vacations. The country shuts down in late June and your emails won't get replies before August as people are enjoying the 18 hours of sunshine of Nordic summers. :)
As for what the "entire point" of a greeting is, I'd argue that the "entire point" is a bit of a philosophical question that depends on what you think it means for something to be "the point". Maybe a few thousand years from now, instead of seemingly ignoring the culture and history you refer to, Solsthelion will just be seen as another chapter in the history of the greetings used during this time of year, just like the cultural reference in one common greeting you might encounter this time of year might have seemed transgressive back when it debuted to people fond of previous cultural traditions during the same part of the year.
It mentions winter and summer, seasons that do not exist for a lot of the world. For example, in South Asia the main seasonal variation is the monsoon rains.