In a nutshell, systematic expository preaching ensures that the Word is preached, the whole Word is preached, and that the pastor has less of an opportunity to rehash his own opinion or stick to a "canon within the canon."
Bryan Chapell, author of Christ-Centered Preaching (which is probably the best preaching text since John Broaddus), says:
The thing that I think is most advantageous in an expository method is not only are we being bound to the message of scripture, but the preacher then has the authority of God's Word with which to challenge or encourage people. That one says: "this is not me as a preacher talking. This is what God says to you based upon what this text means." So the chief advantage, I think, is the preacher is allowed to operate with the authority of what God says.
There are other advantages: if one is dealing in an expository approach -- main points, subpoints coming from the text -- I think you create an informed listener. People who listen to expository preaching over time learn to see how scriptures develop, and therefore their own interpretative skills grow. There is the advantage that the preacher is not bound to his own thoughts and opinions. Particularly if he moves consecutively through a text, he is forced to deal with subjects that might not normally appear to his own mind.
The advantage of that additionally is he can address subjects that, had he thought them up, might appear to have been too pointed with perhaps sensitive issues in the congregation. If he is simply moving through the text, he might be able to deal with the subject of gossip where, if he had simply brought that up as the theme for the week and it had no connections to previous weeks he might seem to be responding to his own hurt -- that somebody gossiped about him and so he was just going to get them back in the sermon this week. So expository preaching has the advantage of authority, has the advantage of teaching, has the advantage of pushing us beyond our own opinions and enabling us to touch sensitive subjects without appearing to pick on people.
By preaching systematically, the preacher also has the added benefit of an economy of scale when it comes to preparation. For any text, one needs to really be conversant wit the whole book, before picking out a pericope. If, however, you stay in the same book for several sermons in a row, you're already immersed in what the single writer is saying.
One cannot stay in a single book forever, though, because to do so will deprive listeners of the rest of the Scripture (hence the advantage of a lectionary, which is not systematic!).