So, the good guys are out. Who are you rooting for in the playoffs?

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.
All coaches that are coming to a new team know the job is second tier. Not many teams fire winning coaches so it's not top tier by that fact. That is why the job is available in the first place. I'd argue a team that's won Super Bowls expects them and it makes the expectations harder to meet than a team that still doesn't have one. It's certainly been the case here.

And I don't see players leaving teams that are playing good football unless they are offered more money somewhere else. Heck, I think WHERE a team is playing is more of a factor for coaches and players than WHO the team is. And a national consciousness doesn't mean much either. Most people live in a place that other people have never heard of. Once you're there, it's just your day to day and national opinion doesn't mean much.