its that the effect occurs on even high strength creatures and can stack. Consider a Lava Golem, as it gets bigger it gets less atytack, keeping total damage under or around 20 until the golem itself is that strong. With this you permanently double and then keep stacking. The effect itself as you have it is a bit too strong.
Consider again a Time Dragon at 10, skyblitz at 9 doubles its attack for one turn, yet you have stackable doubles that may be a bit less each turn, but happen to every creature you have, as opposed to adrenaline that affects 1 creature or Sky blitz that lasts one turn. You are effectively combining two cards for less than the cost of one.
Its not just the cost on this, its the continually stacking extra damage that acts as free Growth on every creature, or all creatures you would take this way. Its just too much.
Now if each card gave 1 extra attack that might work, using extra copies to provide the extra attacks instead of turns in play to, or oif you had each card afect 1 creature like a combination of adrenaline and acceleration, that might work, but as is its just not going to balance.