No, I think that casual titles did well enough on PS2. The thing, though, is that the Wii had some casual titles that sold truckloads, while the PS2 had truckloads of titles that sold some puny amount.
The motto of Playstation consoles in general and especially the PS2 is "quantity over quality". (By quality, I mean sales appeal or whatever you want to call it and not actual "quality".) The PS2 sold tons of casual games that probably went under the radar individually, but collectively made for a huge amount of software sales.
Obviously, though, your argument has some merit as a lot of Wii's casual audience was new to gaming this generation and most of them weren't by any means "inherited" from the PS2.
“These are my principles; if you don’t like them, I have others.” – Groucho Marx
