Yeah see but that's you pulling numbers out of your ass. That's the problem. In the actual game it doesn't work like that. I'm going to not count Runes/Masteries because they could vary and they just make things more complicated.
AD is 35g per point.
AP is 22g per point.
Let's use Talon as a base point cause idk I like using Talon for these things. He has ~68 base AD at level 6.
One Infernal Drake gives 8%, which means about 5.5 extra AD just from his base AD. That's almost 200g worth of stats for free. Meanwhile, to get a similar amount of gold value of AP "for free", you would need.. 108 AP. So you need over TWO THOUSAND GOLD invested in AP in order to just BREAK EVEN with what AD champions get for free at ~level 6. By level 18, you would need 3780 gold invested in AP just to break even. Almost FOUR THOUSAND gold. Oh and that's with AD champions not buying A SINGLE AD ITEM.
Alright so let's take a typical Lucian build since he is the most played ADC. The build has Youmou, Cleaver, IE, and BT as AD items. That gives 255 bonus AD. With his 98 base AD, he would have ~353 AD. One Infernal would thus give 28 bonus AD. That's 988 gold in bonus AD. In order to match that gold value, you would need to get 45 AP. That's about 562 AP needed in order to match that. So you need 12,355 gold in AP to match those stats. While he only needed 8925 gold in AD to get those stats.
It's not balanced.