One would have to directly ask Anselm and Aquinas what kind of God exactly they are talking about...I am not sure they clarified that well enough.
- A mind is a problem solver machine. Why would God need a mind when it has natural order ?...
...lets say that we buy the mind thing for a second:
- Does God has free will ? Can God not be perfect or do other then good ?
- If not then God is not all powerfull and can be put down as the ground of all Being or the Set of all Sets...God as a minor god is just another player that might or might not have created this simulated reality but becomes irrelevant for fundamental Ontological questions.
Moreover if Existence is defined as being the product of intention and mind who created God?
Certainly it is understandable God cannot create himself from his own bootstraps to exist before existing...in that sense an uncreated God concept is equated with the World as concept because the distinction of a mindless mathematical God as pure order, with no degrees of freedom, again, as different from the very idea of a World with mathematical natural order makes no sense. They are equivalent!
Once more, it seems we don't know enough of what to make of a God concept to even be agnostic about it...