It's not quite that bad. From the CA official announcement on this, the AI will reassess what it wants to do every X turns, with X still being unknown. However, it will do this reassessment always on a game load. The reassessment will cause sieges to be broken, and sometimes it will look like a enemy stack found a brewery in the countryside and decided to stay for a while.
At the start of a game, most of the factions will try to take over the rebel towns to expand. Reloading during this time can cause sieges on these towns to be broken, armies to be recalled, and the important expansion postponed, meaning it's easier to beat the factions later on. Since during the early game the turns go by quickly (not as much city management or fighting), if you can go the first 20 turns without reloading, it will make for a better game later.
Once past the initial expansion, people are still uncertain about the best way to proceed. If you can leave the game running all the time (minimized), that seems to be the best approach. Otherwise, try to go at least 5 turns in one sitting. This will give the AI a chance to start and hopefully finish a city assualt.
The posters from the Ludus Magna thread could tell you a lot more (and probably pick apart my poor explanation), they did a lot of research on this.
EDIT - You mention save checkpoints. Just to clarify, I don't think there is a problem with saving the game, this problem only occurs when you load a saved game.
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