Doug Wilson practices a casuistry worthy of a Jesuit when he says that the world is gradually getting better because of the leaven of the gospel, whereas the originator of the leaven analogies, Paul, argued that the world is already very bad and getting worse because of the leaven of sin.
In fact, Paul says that enthusiasm for the Jewish law, which is basically what Doug Wilson's "theocracy" is all about, is itself an insidious leaven which speeds up the ruination of the whole lump.
This is because Paul's main objection to enthusiasm for the Jewish law is that it revives sin and kills us.
But sin, taking occasion by the commandment, wrought in me all manner of concupiscence. For without the law sin was dead. For I was alive without the law once: but when the commandment came, sin revived, and I died. And the commandment, which was ordained to life, I found to be unto death. For sin, taking occasion by the commandment, deceived me, and by it slew me.
-- Romans 7:8ff.
Doug Wilson and his ilk are basically the equivalent of Paul's opponents, the Judaizers.
What is more, Paul is also an apocalyptic and eschatological thinker still emphasizing imminent divine judgment, and Doug Wilson is most certainly not that, either. Paul is concerned with keeping the Christian community in Christ under those dire circumstances, not with making the world a less offensive place for your children's children.
... Basically, what I want to do is agree with you about the part where the Kingdom of God is like yeast that is dropped into the loaf, and it gradually works through the whole loaf, permeating the whole. So when Paul preached the Gospel in Rome, the gladiatorial games didn’t end the following week — it took centuries. But the yeast worked through the loaf, such that the gladiatorial games were ended eventually, slavery was ended eventually, concubinage was ended eventually — all of which was good Gospel progress and postmillennial. That’s the way it works. ...
Yeah, none of that is from Paul, obviously.
Paul's view of living in the world is extremely negative. Wilson's is optimistic, like any good American's, which is the main problem with Doug Wilson.
To Paul, both Judaism's enthusiasm for the law and the world's enthusiasm for sin are dangerously infectious but are made obsolete because of Christ's victory over sin, death, and the Devil. But because human nature remains evil even Christian people are still susceptible to both leavens at the same time. And so Paul is vigilant against the corrupting leaven of them both.
Your glorying is not good. Know ye not that a little leaven leaveneth the whole lump? Purge out therefore the old leaven, that ye may be a new lump, as ye are unleavened. For even Christ our passover is sacrificed for us: Therefore let us keep the feast, not with old leaven, neither with the leaven of malice and wickedness; but with the unleavened bread of sincerity and truth. I wrote unto you in an epistle not to company with fornicators ... them that are without God judgeth. Therefore put away from among yourselves that wicked person.
-- I Corinthians 5:6ff, 13
But this I say, brethren, the time is short ... the fashion of this world passeth away.
-- I Corinthians 7:29, 31
Ye did run well; who did hinder you that ye should not obey the truth? This persuasion cometh not of him that calleth you. A little leaven leaveneth the whole lump.
-- Galatians 5:7ff.
And that, knowing the time, that now it is high time to awake out of sleep: for now is our salvation nearer than when we believed.
The night is far spent, the day is at hand: let us therefore cast off the works of darkness, and let us put on the armour of light.
-- Romans 13:11f.
See then that ye walk circumspectly, not as fools, but as wise, Redeeming the time, because the days are evil.
-- Ephesians 5:15f.