Mindshrieker is a little dude, easy to cast in the first few turns of the game. And he benefits from the kind of high-casting-cost rich decks you find often in EDH games. While a bird-centric deck would be ideal, I think just about any EDH deck (blue, mind you) is going to love Mindshrieker.
Let's play out the bullet points.
1) The pump effect is fairly cheap (2 of any mana), repeatable, and happens at instant speed. You can use it in response to a Lightning Bolt. You can use it after your opponent decides not to block. You can use it after your opponent does decide to block. There is a world of possibilities. A great starry-whorled galaxy!
2) You can use it against yourself, or your opponent, whoever you most want to mill.
3) The milling itself will probably not be a big deal, since it's only one card at a time. And unless its land, your Shrieker is getting pumped by at least 1 and probably much, much more.
4) Here's where the milling might be useful. When deck manipulation (like you might see in the occasional blue deck!) comes into play. Personal Tutor, Brainstorm, even Sensei's Divining Top. Some time ago I went off on a lark and put my ancient copy of Millstone into one of my decks. This seems like the effect I was going for, only much, much more effective.
And regardless of your motives, the Mindshrieker is going to be swinging in or blocking with gusto. Spellbound Dragon is less blind, but you can only do the effect once a per turn. Mindshrieker keeps getting bigger. With the miniscule cost of 2, I am predicting at least a +6+6 bonus every turn Mindshrieker gets into the action.
What a bird!