Think of it like this, if it had no channel time anyone who bought it would just AA and Tiamat active unless they had a swing reset in which it'd be AA, reset, Tiamat. It is a no resource, low cooldown, active that does decent damage and has okay range. It's a matter of giving an item too much use, Tiamat is ment for melee AD damage dealers who want to transition their single target damage to AoE damage. You can use the active for extra damage already, it isn't convenient or for every character. But that's the point.
What most posts seem to say is "I want to use Tiamat active while chasing" which isn't the point of the item. Tiamat users should go in, AoE teams down with AA's and Crescent, and make them weak enough so they have to run or get cleaned up. If you did that, then you used Tiamat to it's full effectiveness. If you want more chasing power, get BOTRK, Youmuu's, any movement speed item, or a different champion. Skarner's Q is ment to allow Skarner to permaslow and beat people up while chasing, that is what Skarner is supposed to do. Riven's W is ment to blast at multiple people or use the mini stun to lock people up for an AA or another spell. Tiamat is for every melee in the game, you can't give an active with such a low CD so much power that it is too useful. That's why DFG got nerfed, reworked, and almost removed from the game.