Waffle batter normally has baking powder in it to cause it to rise, or the egg whites in it have been whipped to make it fluffy.
Bay biscuits... probably don't have as much baking powder in them as they're pretty dense when you dollop out the dough and they don't rise much in the oven.
So while you can make fluffy things in a waffle iron, just because you make bay biscuits in a waffle iron doesn't mean they're going to be fluffy.
They're not as fluffy as waffles, but they're denser even out of a waffle iron. A waffle iron doesn't really compress what's in it, it just moves the batter around into veins, so that veins hold the fluffiness so I don't see why it would suddenly be too dense just because it's made in a waffle iron. The whole point of waffle irons is to get a combo of fluffy and crispy.
Where I live we usually put a batter in the waffle iron, doughs usually get shaped and put on a pan (or put into a loaf pan to make bread shaped bread). All that being said, I'm in the southern US, we aren't known for making sense most the time.
I'm pretty sure waffle irons and clothes irons (and branding irons, and soldering irons) are called "irons" because they were historically just specially-shaped chunks of cast iron.
Iron presses, or squishes anyway. Although just the name itself is not clear really. In my mind am equating it to iron for ironing clothes, so you press the dough into shape.