But gameplay-wise it add problems, like that city that is at "3 turns from you" when it should be 5 turns! Isn't it a real strategic problem?
Erm, no, it isn't because players adapt their strategies to fit a square-based system. Civilization players have been able to handle it for the past two decades.
What is a problem is that a fractional system is that unless it's a real coordinate system, it, among other things, (a) forces units to 'waste' movement points and (b) overcomplicates the simple task of moving units. All of this gets messier given that different units will have different movement speeds, and so certain units will disproportionately benefit from the system and make planning a nightmare.