No, us stopping to do the accounting at the point where the number of moves is even has nothing to do with the game - it's purely a choice of convention for us, so we have fewer cases to consider when doing the accounting. If the number of moves is not even in an actual game, i.e. black has made one more move than white at the point where the last territorially-valuable move is taken and only dame are left, then let white fill one dame before doing the accounting. The again the exact same conclusions hold - komi 6 is the same as komi 5 unless you have one of the rare special cases (odd-dame seki, etc).But in an actual game, where the number of moves may or may not be even, a komi of 6 shouldn't be the same in practice as a komi of 5.
If you don't like that convention, then you can feel free to do accounting directly with black having made one more move than white. Suppose we stop the game at that point, where black is ahead by 6 points on territory, and black has made one more move than white. Then, it must be the case that the number of dame is even, so under area scoring black will get the last dame, ending with having made one more move than white, and again will win by 7 points before komi. On the other hand, if black is ahead by 5 points on territory, and black has made one more move than white, then it must be the case that the number of dame is odd, so under area scoring white will get the last dame, catching to be equal in moves with black, and so black will win by 5 points before komi.
You can see that this case is exactly the same as the other one, except with the reasoning about "odd" and "even" reversed, so that it still comes out that komi 6 and komi 5 are equivalent. The point of stopping the game at a point of equal moves is so that we can not have to do the same reasoning twice with flipped odd and even, it doesn't stop the reasoning from applying to actual games.
Also, all of the above reasoning about komi 5 and komi 6 being the same *also* applies regardless of perfect or imperfect play. The only point where imperfect play comes is in order to deduce that "even" and "odd" are roughly equally likely, it plays no role in the above reasoning otherwise. Obviously with perfect play, it may be the case that 100% of games are "odd" dame, or 100% of games are "even" dame, if the players are always playing the same perfect games over and over, instead of being about 50-50. But the above odd/even reasoning will still apply to each game and make komi 5 = komi 6, so long as that perfect play doesn't involve any odd-dame seki or things like that.