Cain's insight, when reviewed with Myriam, it shows as a possible roll only one of the trifecta stats, critical chance. In the game guide it says that it can roll:
+5 Random Magic Properties
So, could we have in this helmet AS and CC?
When you see the text +X Random Magic Properties, it includes only those properties that normally can roll on the item in question, based on its type.
Helms cannot roll +% Attack Speed or +% Critical Damage, nor can you use Myriam to reroll another affix into those. The exceptions are specific legendaries like Andariel's Visage which specifically list those affixes as things they can roll (and in the case of Andariel's Visage, always roll). Since those are not specifically listed on Cain's Insight, it can never roll those affixes.
So how are you supposed to know which item slots can roll which affixes? Well, the only in-game way I know of is to do what you did and trudge on over to Myriam and eyeball it yourself. But as that's not a very user-friendly process, you probably want an out-of-game source. I recommend checking out this Arqade question about which slots can roll which affixes.