Case and point: My Mom outspent me on gaming last year. She discovered Big Fish and spent $200 in $6 games. The market you mentioned exists.
It exists, and is already being well served. Does the Ouya serve it any better? Not in quality of the hardware. The only thing it truly brings is the TV experience. Will that be enough?
Good question. I don't know.
What I know is that I'm fed up with using my phone to playing games. I need to be at home in order to save that abusive 3G billing anyway, why not leave the phone on the desk and having the fun using a TV?
Having fun using the phone can be expensive. The 3G costs money, and you burns your battery's juicy (and lifespan!).
You will laugh on me, but now when I go out, I carry my Android phone for some Net surfing (google maps, mainly) and Voice calling, and my PSP for the gaming. So now I can play until the battery is drained without worrying about staying offline.