How important is it for a preacher to preach Christ from every text of Scripture?
It's an ambiguous question. Let's see if I can give the two ways I'm hearing it.
It's important that every sermon from a Christian preacher be a Christian sermon, that is, a sermon that, if a Jewish or Muslim person heard it, they wouldn't like. If they like it, something is wrong with it, because they reject Christ as Messiah and crucified and risen as the forgiver of the sins of the world.
And since they reject it, if they hear a sermon that they're totally OK with, then something is missing. The sermon should somehow communicate that this is all based on and aiming toward the work of Christ and the glory of Christ.
However, I don't think there's any particular way that that needs to be made explicit. In other words, when you preach on Proverbs, "Go to the ant, thou sluggard, consider her ways and be wise," you want to preach what's there and show that there are moral lessons to be learned from God's providence in the world.
But you will somehow connect that with what makes you a Christian. You're not a Christian because you look at ants and feel them to be especially helpful morally in setting a good example of discipline. That doesn't make anybody a Christian.
So if you just preach, "Let's all be more diligent because ants are, and God says to," that's not a Christian sermon. Somehow it's got to be connected to the bigger redemptive-historical thing that God is doing that saves sinners and strengthens sinners.
What makes that sermon finish is that what you want in preaching discipline is Christian discipline, discipline that is dependent on the Holy Spirit, discipline that is not earning your salvation, discipline that is the fruit and not the root of your acceptance with God. And all of that takes you to the cross.
So preachers, wherever they're preaching in the Bible, must somehow make it plain that this is a Christian sermon. It has Christian roots and the glory of Christ is at stake. And I think there are hundreds of ways to do that.