The defect Nephi terms "deny the power of God" is an interesting matter to ponder. What do you suppose denying that power involves? How would it manifest itself in the way religious people go about their lives? Is praying without seeking an answer "denying" God's power? Is presuming you have an answer when your own desires are all you are considering perhaps also "denying" God's power?
I reflect on how many times I've learned something surprising, unanticipated, or which had never before entered into my mind. I think, too, about Joseph's comment before his First Vision that "it had never entered into [his] heart that all were wrong" (JS-H 1: 18), but the answer from God informed him otherwise. God's answers are quite often:
When prayer gets through to God and provokes an answer from Him, it is offered with a sincere heart, having real intent. (Moroni 10: 4; James 1: 5.) If a prayer is offered without a sincere heart, and while lacking real intent, is this "denying" the power of God?
If a minister lacks real intent, and does not go to God in mighty prayer, has never become acquainted with the "power of God," but proceeds to teach with their own learning anyway, do they deny the power of God?
In place of preaching what the Lord reveals, men will claim they teach correct "precepts." They have all the revelation they need, and they are now proceeding with the authority given them by God. But they don't hear from Him, don't have new revelation to deliver from Him, and do not expect God to be involved any longer.
In effect, God has become so distant that "there is no God today." He finished His work. He's given His authority to men.
Whether the claim is based on Protestant claims that authority is derived from the New Testament, and all men who believe have authority from God, or it is a Catholic claim to have a line of authority back to Jesus Christ, it is the same. Without some involvement from God in the church itself, the teachings end in the same conclusion: "God has given His power unto men." The institution has taken over. The claim is always that "the church is true" without regard to whether the Lord remains involved, revealing Himself to the church. This is what the Catholic Church has claimed for centuries God has finished His work and surrendered the "keys of authority" to the church. Now God has transmuted into a church, a Holy Roman Church, to which you may confess your sins, obtain absolution for your sins, and have entry into heaven provided to you.
With such a claim, why ask God for help? Why turn to a priesthood advancing such claims? Why make the difficult, inner changes that bring about real intent and faith in Christ? Why seek for and come into contact with "the power of God" if a church can be an adequate substitute?
How like the Catholics have we become?
Was Nephi only warning about Catholic error? Do his warnings apply equally to all?