 Otthers may not find this conclusive, for two reasons.  First, the method doesn’t apply to equations like x = {x}, or to collections like x = ℘fin(x).  The latter kind of equation is especially useful in applications.  But even more, what will be of interest will be the whole assembly of what we might call coalgebraic concepts: coinduction, corecursion, and top-down treatments of various phenomena.  Someone who is using these concepts and is also worried about modeling in set theory would probably find it convenient to work with AFA, even if many of the end applications could be done in standard set theory.  