I think he just flat nailed it. If you have women priestesses, you have something not near so much like a church. The CofE ceased being very much like a church right about the same time it created an order of priestesses.
If Lewis were alive today he would be a great Catholic Apologist.
There was much speculation to this effect during his lifetime and was the subject of at least one letter to Lewis to which he replied rather strongly in the negative.