The majority of american sports fans are bandwagon fans. They flock to the team on top or one close to the top if there is a "feel good" story behind them. George Mason in last year's NCAA Basketball Tournament for example. Now, it's the Saints.
The Cowboys have done nothing over the last 10 years to earn respect with those kinds of fans and as such, have lost all rights to claim "America's Team" .. Americans want to be winners, not average teams. We are all conditioned in that respect.
The main reason for that line of thinking is that growing up prior to the internet (and even cable for some people), most of us were limited to only watching the best teams in different sports on television. Young sports players (aka: recruits) saw those same teams and became fans. So, the stronger teams stayed strong for a longer period of time.
Now, there is so much parity in all sports that there are no guaranteed winners each year. Sure, there are teams that are good almost every year, but again, americans want winners, not "better than average" teams, to root for.
-Reality
