Well, so the story goes, if G.d is the author of all of reality then the human experience is known to Him. And by enter, it would be perfection entering imperfection. A spiritual state entering a physical state. The unknowable becoming knowable, pure abstraction becoming subjected to simplification and objectiveness.
The anthropomorphic god is a human construct. If God, a creator of the universe exists and wants to be known at least partly to us surely he would make himself known to us in a way that we could understand. What else?
Each level of existence somewhat understands the levels below, but not above. As humans we can understand, animal, vegetable and mineral. You can put your bottom dollar on betting that we don't understand those life forms below us, and we don't understand fellow humans. We think that we do giving us this unfounded feeling of superiority because we can do some things that other life forms can't do forgetting that there is a great deal that they can do that we can't do; we can't even take care of our own environment - that is how stupid we are.
As the story goes, G.d need not enter below to know all the levels below. Following your logic, in order for us to gain any understanding of God, he needs to enter our domain. Carl Jung a Swiss psychiatrist and psychoanalyst claimed that God had to enter the human domain and to suffer as a human in order to understand human suffering. He disagrees with you.
