Batman's costume is a disguise with a dramatic flair. It wasn't intended to be armor. Even the gloves where an afterthought, intended to defeat fingerprints. The armor thing only started with Miller, and way too much of his "what if" story was later incorporated into Batman gospel (which has rather blunted the shock value of what he did with the character). Then in 1989 the called the Keaton muscle suit "armor" to get around the fact that it didn't look like real muscle (though I still think it was the best on-screen incarnation).
The SWAT suit he wore in the lat three movies was absurd.
Ah. Well that's different then.