EdDSA is NOT online, but it's trivial to use it in an online way: sign a hash of the data rather than the data. But now you're back to having collisions (EdDSA is collision resistant). So it's a trade-off you have to make. As for DJB's take on this, there were lengthy debates about this on the CFRG list, and you find out for yourself (spoilers: he's very big on collision resistance). Of course, the need for online algorithms is real, but there's more than one way to skin that cat.
Look for posts around June 2015, e.g., with Subject:s like "Summary of the poll: Elliptic Curves - signature scheme: friendliness to low memory implementations" or subjects containing "IUF" (Init, Update, Final) here:
