The Holy Roman Empire's calendar is so annoying. The only reason we still use it is for convenience, kind of like how we still use standard measurements even though metric is far superior.
I think the UNIX Epoch and winter solstice are much better starting points as far as calendar go. The former is what what all modern time measurement is based on any ways in the information age, and the shortest day of the year is a very noticeable and measurable astrological epoch. Calender systems like the terran computational calendar use these as starting points.
There is no good reason for the starting date of the Gregorian calendar. Although it is a well established starting date for the new year, it has no significance today. However, a new calendar year has to start sometime, so it makes sense to stay with the holiday we already have.
The starting point of the Gregorian calendar is arbitrary. However, that does not make it a bad way of keeping time. There has to be a starting point somewhere or there would be chaos. The beginning is arbitrary but the rest makes complete sense. There would be no reason to change it now.