Range Of Variation
A point raised by Thomas under this discussion is that computational claims make predictions about the possible range of variation.
For phonology, what is often mentioned is that if the complexity of subregular grammars are enough to cover phonotactics, first-last harmony is predicted to be not possible, since it requires Locally Testable. (just buzz words for me now)
For syntax/semantics, in the slightest chance that I am right about that the more “complex” a QP is, the smaller a domain is needed on the tier to evaluate scope (height), it is predicted that typological difference could only come from the “complexity” of QPs. I simply do not know enough to tell about whether this is true.