There are a few issues with this approach, though I don't think any are especially serious.

One is that regional authorities may dispute demarcation of their responsibilities. In practice, though, I doubt a police authority and a health board will have much to argue about. And if they do then the national government can step in and tell them who is right, since neither organisation has much independence.

Another issue is that the diagram looks complex. By comparison the other models have a clean elegance to them that atrracts the armchair administrative theorist. This method might work reasonably well -- indeed, it's the method used today for most purposes -- but nobody will ever fall in love with it as a thing of beauty and a joy forever. So it's unlikely to benefit from much zealous evangelism.