I don't quite follow your line of reasoning. Accessible food reinforces behavioral habits, so of course the cage with the food would quickly become their home. How then, exactly, can you quantify that they "love" their cage, as opposed to a large aviary or even freedom to roam in the wild? And I'm not going to make assumptions about your home decor, but most modern homes are neither furnished nor accessibly to birds, posing an immediate danger more than anything. The familiarity and safety of a cage may then be more enticing than flying around a home, and I certainly noticed this behavior in my birds (e.g. loud sounds would send them flying back to their cage in a fright, and in general a reluctance to come out).
The fact that captive animals can adapt to their cages, like a man does to prison, doesn't mean this is good for them nor that it's justifiable. And unlike a man, a captive-raised animal cannot comprehend anything else. You have chosen that life for them and are justifying it.
As for my singular budgie: one outlived the other by many years.