Midwest Express (now Midwest Airlines) have their DC-9s, MD80s & B717s all 2x2 and full service. I think they were profitable every year from deregulation startup until 2001. Weren't profitable for 2002, 2003, but not sure now. Mind you, they aren't trying to compete with AA, DL, UA, etc on the main routes. They fly primarily from Milwaukee & Kansas City.
A couple of others tried - Legend airlines flying from Love Field in Dallas gave it a go, but hit the skids soon after.
Is our market big enough to do this? What is the ideal aircraft? mmmmm, get your thinking caps on.