Christians say

that God could not create a rock so heavy he couldn't lift it, because God's omnipotence does not include the ability to do things that contradict logic. I have heard this argument both from an Eastern Orthodox 4chan anon and C.S. Lewis.

Of course, in Thomism, the argument for God's existence is built on the idea that he is a being that contradicts logic. Everything must have a cause, so there must be a first cause that caused everything else, but that first cause didn't need to be caused, so everything actually didn't need a case.

Whether or not that's a convincing proof for the existence of God, you definitely can't use it and claim at the same time that God is not able to do the logically contradictory.

This is also leaving aside the question of whether there is some fundamental difference between "miracles" and "logical contradictions." The 4chan anon I spoke to insisted there was, without really explaining why. I think Poe's challenge to Mill regarding the tree that is not a tree is relevant here.

So could God create a rock so heavy he couldn't lift it?

Yes, obviously. In fact, that's one of the only ways to explain the numerous inconsistencies in the Abrahamic religions. Why is God, who is supposed to be perfect, depicted as being surprised and having regrets in an account which is supposed to be absolutely true?

The only explanation would be that he limited his own omniscience.

Why don't Christians make use of this argument, instead of denying its possiblity?