Personally, I don't think the time limit should be removed completely. It's always been there as part of Civ, and should be there, but may even a bigger warning than 'game will end in next five turns'. I think a warning of 20 turns, 10 turns and 5 turns would be reasonable, I personally NEVER look at the date, and at one point it was far too late for me
And Elizabeth, we know it's not Civ4, and we don't want it to go on for ever, it's just that on King difficulty, I managed to get faced with a challenging civ, namely the Russians, who I quite enjoyed battling, and my turns ended a bit too soon and without warning (in fact, I reloaded an earlier save, so I don't get a hollow victory, and instead opted for a cultural victory).