The problem is that you are assuming that is only a single form of complexity, while yes the declensions and conjugations have since disappeared in English (and

The problem is that you are assuming that is only a single form of complexity, while yes the declensions and conjugations have since disappeared in English (and most of the West European languages) the complexity of the word order (syntax) has increased substantially. Also, the reduction of the morphological complexity in English PRE-DATES the Norman invasion. So, it had nothing to do with the French rulers. Not to say that they didn't leave a mark on the language in other ways.