There's another issue to be taken with the parabola curve. I'll take Napoleon Total War, as I'm a fan and modder of that, as my example. It's also the direct follow up to Empire TW, so apt for the original example.
NTW is much more preficient at amphibious invasions, than its predecessor ETW. It isn't particularly good at them, but they exist, and have to be acknowledged as a possible threat. Also, the battle ai has been improved (and then improved further by modders), but an experienced player will basically never lose a battle unless outnumbered/ outclassed in troop type.
So you play on the hardest levels, reach the top of the parabola curve, realise the ai isn't really any good, and then that's it. You lose interest right?
Well no, not in my and many other's case. You see, as Psyringe said, if there are enough interesting game mechanics you will keep playing (basically as long as you are still having fun). My point, is to add that for any game I really enjoyed on a long term basis, I make up my own house rules. In NTW, I always insist on having as large a Navy as I can afford, basically to honor a mostly non existent threat. I also try and play as historically as possible.
Europa Barbarorum (something I know very well too)is one of the most popular mods for Rome Total War. Even with all the bonuses the ai is given in its script, the ai is still pretty hapless in battle, so virtually everyone uses their own house rules. Even in Civ IV (after learning and using/abusing every mechanic/slingshot), I played with house rules even at the harder levels. For instance, no troops ever allowed to be built without a barracks (where do they train otherwise?). In Civ IV, a huge amount of the replayability for me was down to the maps, and using random personalities (I could never understand why folks played against the same leaders, time after time...Oh its Gandhi, I don't need many troops....Oh its Mansa, I'll befriend him and us him as a "friendly" research center.) The maps, to me, are always what made Civ what it is/was (delete as appllicable). Having terrain really matter (and I played Civ IV mods which accentuated this), made the game for me, planning out where cities should go was a massive proportion of the fun.
What I'm probably trying to say in this long ramble, is that the Civ series was never really about "beating" the game, and that was what gave it it's 1000's of hours of replayability. It wasn't about having some amazing ai you were constantly competing against, and that's why you never really reached the top of Soren's hypothetical curve. You just started yet another game afresh, with 100's of "what if's" running through your head. The anticipation was in fact what drew you back, time after time.
Anyways, ramble over...............