The problem with that, is you're just shifting the power. Now instead of straight up damage, you're basically giving a team more gold first. Extra damage to minions and monsters means easier to farm means more gold. Now a team has a heavy gold advantage, which is arguably worse.
Likewise, the damage to towers is placed near the end because this is the point when sieging and pushing are very very important. Giving it too early means that one team gets a chance to end the game much much faster.
Short of changing all the buffs, giving the damage first is actually the least of all the evils.
Perhaps but think about it like this
First of all +8% damage helps against minions too
While the +15% minion damage will HELP you CS better, it doesn't GUARANTEE you will CS better. If the opponent is really good at CSing he can probably CS your equal regardless. So there is no 100% promise of an advantage over your opponent
While you can kill creeps better, you are technically still equals when it comes to skirmishes and trades. It takes time to generate that additional gold from the CSing boost.
There is still counterplay options for your opponent as they can still deny you from CSing, either by trading when you go to CS. Pushing hard and try to force tower to steal your CS, especially effective if they CC you when you go to CS.
+8% Damage on the other hand provides your entire team with an instant offense increase over your opponent that can be exploited in dozens of different ways.
They can use that higher offense to win trades forcing you to back more often or use more potions.
They can use it to push team fights and engagements in their favor to earn kills.
Kills which I remind you not only provides your opponent with gold, but also denies you of gold while you are dead.
They can use it to siege your towers faster, killing them quicker than before.