Crusader Kings has/had the opposite problem, with the number of characters getting out of hand and everything grinding to a crawl late in the game (I have played only a moderate amount of CK and am certainly no expert). With Imperator they tried to pre-empt that, but clearly it worked a bit too well.
It's a difficult balance I think. Too many characters is almost more of a problem than too few, since the game does have solutions of adoption and creation of characters through event., even if those solutions are imperfect.
Even a small increase to character survivability and/or reproduction rate has the potential to snowball. As a simple demonstration, imagine that the system is balanced so that characters have an average of 1.5 children by the age of 30, giving almost 10 generations during the game's time frame. For 1000 characters at game start, they would have 1500 children, who would have 2250 children, and so on. You'd reach almost 58,000 by game end, not including existing characters who don't just die when they have had children. Increasing the average birth rate to 1.6 per person gives you almost double that, around 110,000 in the final generation.
I know these numbers are very rough and ready, but it just demonstrates how a relatively small tweak can have an significant impact. I do agree that it's not quite right at the moment, though.