Well, there is of course the so called "Armor of God"
But seriously the whole thing is modern interpretation of early quotes. I seem to recall reading somewhere that the whole justification for angelic wings is from some passages in the Apocrypha about them flying, and early church fathers deciding that, if they can fly they must have wings (which, to me at least always made the story about the Inquisition arresting El Greco on the grounds he'd painted his angel's wings wrong a little funny.) The rest is sort of modenization; adapting the image to current versions of the items being discussed. It's a bit like if you look ad Medival church art of angels with thier "firey swords" the swords more usually resemble then current longswords and broadswords than the leaf bladed kinds that would have been current in the Holy Land Area when the passages were being finalized. Milton and Votaire put armor on thier angels because at that time armor would be part of what a warrior would wear; it's part of the image, whether or not it's still useful, like a US Military officer's dress saber. Either that, or if you want to get a little silly, as time has progressed and our weaponry has gotten nastier, Angels who need to appear to people in combat conditions have needed better and better protection to stay safe (I imagine that, after the little stunt at Mons in WWI, many angels might have felt they needed gas masks).
Personally I've always imagined Balrogs with armor. At bare minimum they'd need some sort of belt, to hold thier flaming swords and whips when not being wielded (they presumaby have to put them down to use thier hands to do other things, like eat). My mind tends to go for the "cuirass and shoulder guards" look, since it tends to fit with my mental image of a balrog (sort of a cross between demonic human and leonine (they have manes, right) I tend to not imagine they have leg armor but that's becuase in my mind the bestial aspects tend to come along with an image of more animal like legs, so that Balrogs have that somewhat bowlegged stance one normally associates with other animal hind legged monsters (like some forms of werewolf) and those don't really fit with much armor.