Perhaps the simplest reason for killing off everyone we knew in CT (while not definitely killing a single one) is simply to explain why they aren't worked into the story, and it puts more emphasis on the current party. If Crono & Co was around, really, would there have been anything for Serge to do?
Given that for everything that happens, there are at least a million different ways the course can go, the operative theme of CC was an infinite amount of dimensions, though you really only travel between two, due to Serge's special case.
Actually, CC seems like it argues for a very limited number of dimensions. Indeed, only two are known to exist for sure, with the reptite/dragonian dimension being unclear if it is a full dimension or temporal leftover from a previous change to the timeline. The game places the cause of the split fairly squarely on the 50/50% chance of Serge dying or not, something that doesn't seem like it would be overly common. But as the good Mr. Bekkler pointed out, there's only one dimension that we even know they don't exist in.
The year 1000 A.D. was a little too peaceful. We knew nothing about Guardia's founding or why it was important enough to establish its own calendar.
It didn't establish its own calendar, though to be fair it does appear from 600 and 1000 that the kingdom was roughly founded around the turn of the era, give or take a century. As for it being peaceful, you are forgetting that the mystics tried to dethrone King Guardia XXXIII. And that Guardian military tech has decent enough funding to create the dragon tank (indicating that there are other militaries out there to potentially use it against).