I be would argue that it does affect the franchise.
It affects the coaches that see a franchise with no Super Bowl(s) as a second tier job.
Players that get out the moment they can.
Borderline HOF players wanting out because a half century of mismanagement will put a stain on their careers.
A franchise that has no identity in the national consciousness.
A Super Bowl changes the perception of a franchise.
Heck, the Saints are still benefiting from XLIV.
It’s no coincidence that Saints starting getting into the Hall the year after the Saints won a Super Bowl.