They have no AAA team because Louisville is in their region and is doing really well as a franchise. (Top five in all of minor league baseball over each year since 2006.) Moving Dayton to AAA (assuming the International League would allow it) would actually cost the Reds money. And interest.
We seem to have this discussion every few weeks.
"You can learn little from victory. You can learn everything from defeat."
-- Christy Matthewson
"Show me a good loser and I'll show you an idiot."
-- Leo Durocher