I blame it on lazy programming, or incompetent programming, either one is something I could see New Vegas suffering from, judging from the amount of bugs in it. I'm also fine if companions without power armor training being unable to wear power armor, I guess it's not unreasonable that if the player needs proper training to use power armor, companions would too, I'd be perfectly fine with these things if the companions just refused to wear these armors, but they don't just refuse to wear them, you try to give them these armors to hold, and they drop them as though they were radioactive.
It seemed to me that the entire point of the faction armor system was to let players disguise themselves as members of other factions, and if players can disguise themselves, why shouldn't they be able to disguise any companions traveling with them, but that's beside the point. And they're willing to carry everything else you give them, it's just armor that they're not able to wear, usually faction armor, though power armor qualifies if they don't have power armor training too, and really, I don't mind if they refuse to wear the armor of factions they don't belong to, even though it kind of strikes me as a bizzare choice. They have no use for scrap metal either but they won't drop it if you give it to them.
They can't use it, so it's of nu use to them.