As a male, I think I can give a bit of input, my opinion anyway, to the question, "Why do men like to be caged".
I can't give an easy answer, even if there were just one. But I can tell you what mine is. I was married for many years. My late wife and I had a wonderful life in the bedroom and in the world. Unfortunately, I never had the bravery to tell her about my thoughts about using a cage. I can’t know her opinion, but bondage was mutually enjoyed. I bought my cage too late to share with her. But, back to the question.
In my case, I love the ability to be reminded of my submission and loss of the choice to change my mind about it. I believe I have always been a submissive and my cage is a constant and undeniable reminder of belonging to my keyholder. It removes all of the inhibitions and socially imprinted expectations of my male position in a relationship. As a man, even one such as I, who believes women are superior, we have been conditioned to believe the man should have the final word. Although I always try to compromise the best I can but my GF or Wife will always win.
Again, back to the question, the cage gives the keyholder the power to have us do anything she wants while removing any excuse we may be able to think of to object. Thereby, it frees me, allows me to bow down, and give all to her. That feeling of freedom is priceless to me.
(I love being owned by a woman, and the cage reminds me of my position constantly.)