This is well-worn territory.
In 2012, APC discussed why it would never happen. A year later, the Press-Gazette said the same thing.
So, I guess it's clear that it'll never happen.
But wouldn't it be interesting?
As a Packers fan, I don't want Titletown to be the feature of 'Hard Knocks', and I've argued this before. It sets the wrong tone for rookies, gives normally-classy veterans a reason to act out, and offers nothing more than a distraction for the coaches intent on preparing the team for a Week 1 matchup which will contain enough distractions in itself.
And the Packers are allowed to opt out assuming they've clinched a playoff berth in the last few years; in the Rodgers era, that's an expectation.
"Hard Knocks' isn't just produced for the benefits of the team's fanbase, however; the drama of training camp is to appeal to NFL enthusiasts (and folks just interested in watching the closest they'll ever get to gladiatorial combat). So let's look at a theoretical situation in which the Packers did appear on 'Hard Knocks', and why folks across the league might tune in.
Aaron Rodgers is an entertaining guy
If you've seen Rodgers' photobomb album (and, in Stephen Colbert's words, I hope you have), you'll understand what I'm talking about. From his post-game interview after the Packers-Texans game in 2012 ("shhhhh") to his comments on Juwan Howard (aka 'Juwanna Man'), he doesn't take himself too seriously off the field. Watching him (and his perhaps augmented training camp antics) would make for good television. Would it help the team? Probably not. Does HBO care? See response to previous question.
Matthews-Peppers combo will garner attention
The logical ones among us realize that Julius Peppers is an effective situational guy at this point in his career. The directors, however, will likely focus upon his hulking frame and the fact that he's the most high-profile signing we've had since Woodson. Any time he blows past an offensive lineman, camera crews will be paying attention. Add that to the flowing hair and pure explosiveness of Matthews, a top pass-rusher when healthy, and there's plenty to excite viewers.
Battles at center and tight end
The center position, as we know, is a critical one, as the starter must built a rapport with the man he's snapping the ball to. When that guy is Aaron Rodgers, there's reason to care. HBO can portray Linsley and Tretter as opposites- Linsley is the hard-nosed guy who's faced off against great competition, while Tretter is the quiet intellectual with the work ethic and athleticism to take the position.Throw in Don Barclay potentially moving on, and there's enough drama here to pique the interest of the average Joe.
Tight end should be even more interesting. How often does a Super Bowl starter get supplanted by a third-round pick or an undrafted free agent? And how often do the high-character Packers take a chance on a guy who got kicked off his high school football season and continued with his off-field issues? Watching Richard Rodgers (Rodgers-to-Rodgers connection will be discussed ad nauseam) and Colt Lyerla work to unseat Andrew Quarless from his starting job would be fascinating.
Multiple receivers, Bulaga enter contract years
The Packers' top three receivers- Jordy Nelson, Randall Cobb and Jarrett Boykin are all in the final season of their respective contracts, as is Bryan Bulaga. All except for Boykin (barring a monster season) are in for sizable paydays. While the expectation is that all three are retained (and none of the players are known to complain, at least publicly), you can bet that HBO will take any missed block or dropped pass as a sign of dissatisfaction on part of the player. Add in the fact that contract negotiations might occur during this period? Grab some popcorn.
Attitude change on the defense is inevitable
The Packers need to prove that the D is tough. The safeties didn't force a single turnover last year. The defensive line was ineffective save for the pugnacious Mike Daniels (who would also be a highlight of training camp.) Dom Capers is on the hot seat, and if he isn't, that's a headline in and of itself. Expect to see some hard hitting, and maybe even a fight or two. It's time the defensive shows that it won't hold back the offense, and capturing that on television would probably tickle the producers pink.
So, there. Five reasons that the Packers would be great on 'Hard Knocks'. There are far more reasons why it's not feasible (or beneficial for the team), but, hey, it sure wouldn't be worth sleeping through.