It also doesn't make a lot of sense from Othello's perspective. Iago is able to play on Othello's weakness, and the only reason he's able to do that is because Othello trusts him so much. Since they're long standing friends, I have trouble believing that Othello would be so blind as to not see that aspect of Iago's nature, if it were really there.
This is where Iago differs for me: With all of the other Shakespearean villains, I can see where they're coming from (especially, for instance, someone like Edmund in "Lear"). With Iago, though, not so much.
In a way, that makes him all the more frightening but it also means he kinda sticks out in an odd way compared to some others.