Mage are not weak, but the gameplay they currently have doesn't fit what a Mage should be, a Support
The reason why we want mages to have better itemization is to push them away from the boundaries of being a CC Support who's job is to assist the Jungler or Peel the ADC.
Mage should be by itself a Role that stands out as a Magic Dealer and not a Support with CC. By itself it should be a core part of the Team and champions should be able to build around the mage depending on their Gameplay.
Take for Example Kog Maw, where there are Team comps that are specifically created to protect him from harm. You cannot do something like that with a Mage such as Brand, Aurelion sol as they are all based on landing skillshots and ditch out inconsistent damage depending on what they face. If they are facing a High mobility Assassin they are most likely not able to land any skillshots and they might feed their lane and fill a secondary support role for Late game, as their build are extremely expensive and require more gold than an ADC.
The thing about an ADC is even if you miss all your skillshots, you still have alot of power into your Auto Attack making your champion a little too reliable in term of Damage because your itemization basically just enhance your Auto attack. Even if your champion is squishy you have itemization that basically deny this weakness such as
and any lifesteals item. You have active items that basically makes you immune to cc for a short sec like
, aswell as
which helps you win trades against AP champions.
So what we want is basically, Mages Itemization that enhance their abilities at doing damage, Let's give an example, If there is an Item that enhance a Mages Team Fighting capabilities such as laying landmines to the location where your Mage abilities hit with a 10sec cooldown. So for exemple if your Brand hit someone with W, a couples of landmines appears on the ground. It doesn't necessaries give more Damage but cripple the movement of your enemies. So Basically they won't side step Left but will rather sidesteps right making them much more predictable and help the mage to predict the location they are going to walk to. Survivability depanding on Offensive capabilities such as Lifesteal, Tank Killing potential, Especially for Late game, Itemization that helps fill out the weakness of certain mages, Such as Viktor not being able to land his double E consistently since the 2nd hit of E as a big delay on it.