Neck-dive is way low down on my list. But I also have come to appreciate each instrument for what it is - I have several instruments that are far from perfect, but they offer something special.
I stopped playing for about five years - when I started again, I read a story of a guy with a beautiful Rickenbacker who was standing around after a show with it just hanging on the strap - the strap came off and it hit the ground. Made me conscious of the possibility, and I basically never let go of the neck if I can help it - somehow I trained myself. Thinking about it now, that bass must not have had much neck-dive for him to just let go!
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I would think a lot would depend too on how much you play and in what circumstances.
Now I have to play my current #1 and think about it. Or maybe I shouldn't if it doesn't bother me!