You're conflating different meanings of explain: on the one hand, to describe in terms of predictable patterns of behavior; on the other hand, to satisfy the principle of sufficient reason.
Specifying a cause is always more complex in the sense of multiplying hypotheses than omitting a cause. "There is a kitten, and the principle of sexual reproduction explains where it came from" is more complex than "There is a kitten." It's just epistemically irrelevant.
No amount of kitten studies will change this formulation, because all the adjectives you pile onto kitten are going to get packed into both "there is a kitten" statements. We'll just have "There is a (long description) kitten, and the principle of sexual reproduction explains where it came from" versus "There is a (long description) kitten."
It is not possible to explain the kitten (describe the kitten in terms of predictable kitten patterns) well enough to explain the kitten (satisfy the principle of sufficient reason why there is a kitten).
Even if you study the kitten sufficiently to form a hypothesis about the reason why there is a kitten solely on the basis of the kitten's nature (i.e. by watching her grow up and reproduce, or by doing physical chemistry with a time-reversal operator to trace each molecule to its origin outside of the kitten), the reason why there is a kitten will inevitably describe something other than the kitten: an entity or entities outside the kitten and in some way higher up a hierarchy of necessity than her.
At this point, we're comparing two "There is a (long description) kitten, and the explanatory principle is..." statements.
If we have enough data, we can do Bayesian calculus with countable measured frequencies for priors and make reliable statistical predictions that we can all agree on.
Or we can make up arbitrary definitions of "complexity"... and quietly discard any which don't turn out to lead to our desired conclusion before we publish... while our interlocutor does the same with a different desired conclusion and different arbitrary definitions. Then we can have a drawn-out go-nowhere Complexity Fight over who has the Burden of Proof, based on one of the sayings of a 14th century monk whose authority we reject on all other topics, instead of actually presenting any arguments in favor of our claims. This is absolutely guaranteed to accomplish nothing whatsoever, but we can probably collect salaries and citations for doing it. Hurray!
Note that this concerns differences of explanation, not differences of description. It is entirely possible that our descriptions of the kitten will differ. For instance, I might believe that the kitten can adversely affect gambling probabilities by crossing a person's path, while you might not. At this point we can start collecting data and doing statistical analysis to figure out who is right.
