Animation Cancelling for Melee a myth?

seriously don't get why people bother with animation cancelling on melee champs. I can understand why it would work on ranged because there is still a sliver or time period after the projectile has been launched, and by cancelling this animation you can carry out the next auto attack quicker. But it case of melee champs it doesn't necessarily work the same way. In fact in most cases, the damage is dealt when the animation ends (i.e. the champ has finished swinging the axe, sword, etc.) Any animation that happens AFTER is that where he takes his sword back and swing it again. Now here, the amount of time it takes to swing the weapon back before bringing it down to hit again is taken into consideration ALONG with the attack speed. That is, even if you cancel the last animation, the next attack will still take as much time as it would have if you had just clicked once and let it auto attack on its own. It also often happens that in the process of such micro management (which often really makes only a negligible difference) you cancel the auto attack before it lands, resulting in just the animation but no damage because you cancelled it and making him swing his weapon again. So, how many of you believe that the importance of learning AA animation in melee champs is bullshit? P.S.: Please if you disagree give a proper explanation because Im finding it difficult to wrap my head around this concept? I can understand how it may affect Ranged champs. But what about melee?