No, you're pretty much right. In fact, if you exclude Mammoth Cave NP, we don't have a lot of real "caves" in our hiking areas - they're mostly in the nature of scooped-out, open-front rock shelters, eroded by wind (mostly) and water (somewhat) back into a cliff.

They're usually damp, and dank, and really not very pleasant to camp in - unless you're 22, a mile from the parking lot, and alcohol is involved.