I have been in the work world for well over 30 years and I have seen a lot of good managers, a lot of bad managers and a lot of mediocre managers. None of the good managers manage to some sort of management theory exclusively. Most of the bad managers do not either (some of them apparently have no management style whatsoever except "how can I push the blame off on someone else") but virtually all of the mediocre ones do.
He needs to manage the situation not the theory. If the organization is comfortable with the type of management they have, and is working effectively, then don't change it. Otherwise he will cause performance to get worse.
If they are not effective, then find the specific things that are causing the problem and make changes according to what you find. They may need more control or they may need less. It often depends on the regulatory environment and the specific types of work to be done and most importantly the personality types of the people. For some people Theory Y management is like a being in a torture chamber. Others like it. As a manager, he needs to go with what is best to get the job done, not with your personal preferences. Sometimes that is a mix of both. OR the problems may be that some incompetent people need more control and some others who do their jobs well need less. Or maybe he just needs to get rid of some people of fix some broken processes that have nothing to do with management theory such as an ineffective or nonexistent process for managing task prioritization (or even knowing what tasks need to be done).