Preference
I look back at "higgs'" comment. What bothers you and your crew most? The wind and spray, or the sun?
We sailed Lady Lillie for a few summers on Lake Erie without either a dodger or a bimini. We (the Admiral and I) were sure that for us it was the sun. Eight summers later, we still like that decision. And, a dodger has not even been nominated for our "to do" list, although we push sailing well into the cold days of the fall.
My thought after reviewing this thread, is that our preferences can be very different on this issue. As higgs indicates, it seems to be personal. The Admiral and I started sailing in a Moth and a Sunfish. Wind and water were attractions for us, and are part of our enjoyment today. Despite sailing over 6,000 nm's, we don't often pound into the wind and waves, and our boat is quite dry when we do.
I hear that a lot of us would be unhappy in our cockpit with us. I'm OK with that, and enjoy sailing on our best friends' Hunter 30 with a full dodger. So I think our preferences are key to this question.