Math, indeed. Although I don't disagree, there's a slight oversight here.
You are correct in saying that attacking 1.5 times as fast without AD is useless. However, when you are deciding between AD and AS, there's a tradeoff you have to make. One option is, as you said, to take AS without AD. The other is to take AD without AS.
So I could say 'what's the point in dealing 1.5 times as much damage without AS?'.
Let's delve a little into the math here.
We can all agree that DPS = Rate of Fire x Damage Output
Putting this in League terms:
DPS = AS x AD
And so, both are theoretically equally relevant to the overall equation. Having more AD at the expense of AS will provide more burst per AA while having slower AAs and having AS at the expense of AD will provide more AAs in the same amount of time while having them individually be weaker.
At the same time, what this equation calculates is a lot more useful for late game when fights are much longer than five second long early game trades. AD is almost always superior early due to more raw damage per AA poke.
Now what I wonder is that for some on-hit ADCs (like Ashe), would AS earlier on be more useful? Being a pathetic ADC player myself, I'd like to hear some opinions on this.
Wow, I have no life. I guess your comment triggered my inner nerd.
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Oh wait, I am a nerd.