There are different types or "levels" of allegory. Some are stricter, and others are looser.
A frequently cited example of the strict type of allegory is The Pilgrim's Progress by John Bunyan (1678).
The Pilgrim's Progress is a story about a man named Christian who is trying to get to the Celestial City. He takes directions from a man named Evangelist, is almost led astray by Mr. Worldly Wiseman, teams up with Faithful and Hopeful, gets captured by the giant Despair who traps him in the Doubting Castle for a while, etc., etc.
Every person and event in the book is a stand-in for one particular thing or concept, and nothing else. It's like one of those political cartoons where everything is labeled. Bunyan wants the readers to know exactly what he is getting at in every scene, no more and no less.
This, I believe, is the kind of "purposed domination of the author" that Tolkien rejected.
Certainly, you can draw connections between the Lord of the Rings and, say, Christianity or the World Wars. There are parallels: some were conscious on Tolkien's part, some were presumably unconscious, and some were completely accidental. But the story can stand on its own two feet without them. Gandalf may be like Jesus, in that he sacrifices himself and is resurrected, but he is not a stand-in for Jesus; the Ring might be like an atom bomb, in the sense that it is a unique and dangerous weapon that could turn the tide of a war, but it is not meant to represent The Bomb and nothing else. (Actually, it wasn't meant to represent The Bomb at all. That's one of the accidental ones.)
The point is that you don't have to be "in on the joke", so to speak, to appreciate Tolkien's work.
I prefer history – true or feigned – with its varied applicability to the thought and experience of readers.
History doesn't demand you read it in one particular way, even if the people living it out had some very definite interpretations in mind. It is complex enough to allow for analysis and debate and multiple interpretations, as opposed to a dreary game of "Oh, X is meant to represent Y." The Lord of the Rings is very much a "feigned history", which is what makes it so enduring. With a work like Pilgrim's Progress, the reader gets the distinct impression that nothing exists, or can exist, outside the immediate demands of the author's symbolic scheme. The Lord of the Rings, quite simply, feels more real than that.