I can't discredit the Patriots. They are the best dynasty ever. But I do agree with your other points. The Ravens took 16 years before returning to the Super Bowl and beating the 49ers in their first appearance in nearly 30 years. The Bucs and Raiders are in purgatory. The Panthers had about a decade between Super Bowl appearances. The Eagles had their first Super Bowl appearance in decades. The Seahawks had a stretch between XL and XLVIII. The Bears one playoff run in a decade ended in a loss at the championship. The Cardinals? That was their one shot, stopped by the Steelers. The Saints won in '09 and had a hopeful run end in '11. The Packers had 1 Super Bowl appearance in the past 15 years. The Broncos had their appearances and 1 championship since the late '90s.
In that span, only the Patriots (4), Steelers (2), Giants (2), and Ravens (2) have had multiple championships since '01. And the Colts (2, 1-1), Seahawks (1, 1-2), Panthers (0-2) have multiple appearances with only one or no championships.
The point? Just getting there is tough. And note, this leaves notable franchises like Washington, Cowboys, Vikings, Dolphins, 49ers, Raiders, and others with no championships this century.