I agree with you. I'd rather have no prayer than a government enforced, non-sectarian prayer.
Actually, I have no problem listening to a Catholic priest being himself and offering a more thoroughly catholic prayer. At least I know I'm getting an honest supplication.
And I have absolutely no problem with an honest Church of God or Southern Baptist preacher praying from his heart. I may not agree with every detail of his doctrine, but the main point is "Jesus Christ, and Him crucified."
And as dear Mr. Franklin said, we must all hang together or we will assuredly hang separately . . .