tl;dr version: Because trapped armour exists, most armour in my games never gets identified or used, and the other prefixes and suffixes are almost never seen in my games. Full reasoning below, please have a read.

I recently had a game in which I made use of some clothes of travelling that happened to be in my inventory when I read a blessed SoID. I thought 'wow, these are really handy, I should ID random armour more often', but then I remembered why I never do:

All I really care about from body armour for the early game is PV without any huge penalties. Later immunities (dragon scalemail) and DV start to matter more, but mostly it's just PV. That makes clothes and weaker armours fairly useless, and horrible to get stuck in. Ever since getting stuck in trapped clothes, I have never mass equip-ID'd armour, because the risk to reward is far too great. There's never a tremendous benefit from finding a 'nice' set of clothes or other weak armour, but getting trapped without a scroll of item destruction is at the least a colossal nusience, and at worst is game-ending. Typically I'll only equip-ID 2-3 sets of armour in a game; the first (studded) leather armor I find, the first decent set of metal armour I find, and then some dragon scale mail.

That leaves magical ID. The Identify spell is scarce and largely restricted to proper casters; and in any case, by the time they have it, they likely have such good armour that they don't care to randomly ID everything other armour they find. Then there's scrolls of ID, but armour is so heavy that it's just not worth carrying around a ton of it in the hope that there might be something decent in there.

In summary I think the existence of this prefix stops me experiencing all of the other prefixed and suffixed armours in almost all of my games, and I think the game would be richer without it. We'd still have auto-locking which is similar, but is at least countered by holy water.