Both the ultraweak and ultrastrong topologies are intrinsic topologies in the sense that the image of a continuous (unital) $*$-homomorphism between von Neumann algebras (in either topology) is a von Neumann subalgebra of the target von Neumann algebra, unlike say just norm-continuous $*$-homomorphisms. One may then speak of the category of von Neumann algebras with morphisms as ultrastrong $*$-homomorphisms.

Why do we predominantly think of the ultraweak topology as the intrinsic one when presumably there could be many more topologies that are intrinsic in the above sense? I understand that the ultraweak topology is the weak-topology coming from the pre-dual and hence quite natural to study. But is there a guiding logical or category-theoretic principle that tells us to make this choice?

Thank you.