Logic stays. Alogic fails. It fails, because it is wrong and weak. Logic is based on a causal relationship, which is a result of the action of laws, which are the result of the action of intellect, which speaks of order, organization, connectivity, interdependence and so on.
Alogic is disorderly, contradictory and conflicting, and even when it can exist it exists in a chaotic, unpredictable and even hurting way depending on the degree of discord and opposition.
To create the world so that it should exist is much more logical than to create it in order to destroy it or let it perish. This would make all the efforts pointless and attribute to God qualities that He doesn’t have, such as stupidity and short-sightedness. The complexity of man and the creation speaks for exactly the opposite ― a high level of intelligence, ingenuity and far-sightedness. In order to be able to create something, one has to have the knowledge, skills and resources for creating it, and the very presence of the thing created proves that one has them. And if the created thing is complex, well-organized and governed by laws, then the assumption that the one who has created it is also like that, but to a much greater extent, is a lot truer than the assumption that He is not.
All in all, God would not create something that could be defective or ineffective because He is perfect. The “ineffective” part from the human point of view is “effective” from God’s point of view, because it executes a part of God’s plan, which ― although done in violation of His will ― follows logically from the freedom He has given to some of His creatures (including man).
To save something that already exists (especially when it is not only bad but also good), is also much more logical than to let it regress and become waste. To destroy good together with evil is unjust and God is not unjust. And we cannot but agree that there is a lot of good in the world we live in.
“The Lord by wisdom founded the earth, by understanding He established the heavens. By His knowledge the deeps were broken up and the skies drip with dew” (Proverbs Chapter 3, Verses 19 and 20).