Well done! Yes, it's about loss. I felt that so intensely, reading about the elves leaving Middle Earth, a melancholy suffusing my youthful spirit.

One thing you don't address is Tolkien's unhappy childhood as a near-orphan from (at the time) a poor family, not quite in the class of his peers.

His isolation in youth led him into his fantasy world. He sought a world where bitter reality could not penetrate, unless it was transformed into myth. Inside myth, he could escape.

In his later adult years, it's ironic how much of the real world (though transformed into myth) made it into his personal escape. There's something 100% real and 100% fantasy in LOTR. That might be what makes it so compelling.