First, let's clear up a misconception.
Armor Penetration gives you a constant %damage bonus, regardless of how much armor the enemy has see here.
It doesn't matter if your enemy has 300 armor or 15 -- penetrating 10 of that will have the same effect on total DPS increase.
That said, let's take a look at why Armor Penetration is preferred, even with its linearity.
Attack Speed is easy to acquire via items.
Armor Penetration is not.
You can more than match the effects of attack speed runes with a single dagger - 420 gold.
The cheapest item with Armor Penetration is the Brutalizer at 1337 total gold. By this metric alone, Armor penetration runes are worth approximately three times that of attack speed runes.
It is easier to use items to stack Attack Speed over Armor Penetration -- but to get the highest DPS, you want to stack both.
Given that the amount of Armor Penetration available via items is strictly limited, if one's goal is to achieve maximal values for both Armor Penetration and Attack Speed, runes for Armor Penetration are much better than that of Attack Speed.
In Crs SYDTKOs' guide on LoLPro he says
"Cho'gath, Galio, Morgana and Ziggs but note that Cassiopeia is such a strong champion, these are just things that farm incredibly well against her without dying; there are no champions in mid-lane that 'counter' Cass."
This opinion was also shared by Dignitas' Scarra on his stream a few nights ago.
So according to the pro players, she is so strong she doesn't have a counter per say, but the best you can do is farm against her and hope she makes a mistake. Hope this helped.
Best Answer
Doran's Rings give you an early lane advantage. While they don't build into anything later the way that a catalyst or a blasting wand might, they immediately give you health, mana regen, and damage. Short term, Doran's Rings give you better value for your gold than other items.
The most common reason If you are playing aggressively AP, you can use these items to generate a lane advantage that turns into kills or a significant farm lead. For example, if get a kill because you were tankier and did more damage than the enemy AP, the Doran's ring has paid for itself. Also, the rings might provide you the mana to spam your clearing ability on a hero like Morgana or Ahri. As a result the enemy AP loses farm to their tower and your ring pays for itself by costing the enemy gold.
If you are going to play passively and farm (Karthus, Anivia, etc.) then Doran's are likely not the right item for you.