Let's be more precise...
America's Team is not an annual reward or an award for the decade. It's a nickname for the Dallas Cowboys... for as long as the Dallas Cowboys remain the most valuable franchise in US sports, which is a function of their ability to drive advertising and merchandise sales... which is a function of their national, and even global, popularity.
That objective measure has been incredibly resilient over time, even weathering stretches of below-500 teams on occasion. How long will this persist? Who knows? No one knows. But it is highly unlikely to drop off a cliff... if it happens, it will be a gradual regression.