Out of curiousity I took a look at some midflight photos as well as slow mo videos. It could also vary by butterfly type, but there were definitely midflight photos were I saw wings quite extended front. Also in slow mo it almost looks as if they are swimming through air where they extend wings front to grab air and bring them back down. I suggest taking a look at some slow mo videos. It now occurs to me why there's a swimming technique called butterfly. The animation in the web app doesn't do the swimming technique justice, it's rather static, but at least I do think at certain point they have their wings quite extended, so unless you animate this whole thing, I don't think it's as fair to call it dead compared to if it's standing by with wings extended.

That's fair -- to something as small as a butterfly the air is much more soup-y, so swimming is maybe a better description than flying. That would imply they do need to extend forward beyond their head to pull forward through the air.