The problem is that a lunar cycle is about 29 and a a half days. So for example if your ancient city-state establishes a day for a harvest festival in the 3rd week of the 10th month, the difference between a revolution around the sun and the time lunar cycles take will cause that date to drift and eventually no longer be near harvest time.
So basically the Roman civil calendar was all jacked up towards the end of the republic. Caesar consulted with an Alexandrian astronomer and came up with a modified version of the Egyptian solar calendar, adding that quarter day. And as a bonus fun fact, archeologists can't agree on how old the ancient Egyptian 365 day calendar was. But they also had a lunar calendar and apparently used both. So solar vs lunar is an unknowably old debate.
The problem is that a lunar cycle is about 29 and a a half days. So for example if your ancient city-state establishes a day for a harvest festival in the 3rd week of the 10th month, the difference between a revolution around the sun and the time lunar cycles take will cause that date to drift and eventually no longer be near harvest time.
So basically the Roman civil calendar was all jacked up towards the end of the republic. Caesar consulted with an Alexandrian astronomer and came up with a modified version of the Egyptian solar calendar, adding that quarter day. And as a bonus fun fact, archeologists can't agree on how old the ancient Egyptian 365 day calendar was. But they also had a lunar calendar and apparently used both. So solar vs lunar is an unknowably old debate.