Well, in 2005 through 2009 Brady’s contract gave his team one of the four biggest cap hits in the entire league in four of those years, and in the fifth he ranked number eight in that category. That contract was his second extension, but in reality it was an upgrade on his previous deal that he only had for two years. However, it meant that he got two signing bonusses, and with each of them he apparently were willing to give the team a huge cap hit. I only bring this up to show that he too was looking out for himself first and foremost before he became the superstar he is now, and by the way, before he got married. Now, you are obviously correct that the situation has change in the latter part of his career. I don’t know why. Maybe it’s because of his wife, maybe it’s because of his many endorsement deals, or maybe it’s because he still makes millions of dollars and have decided that he wants to win above everything else. There’s even a theory out there that the team owner, and Brady’s close friend, Robert Kraft has promised to compensate Brady heavily when his career is over in return for Brady lowering his contract demands now. Whatever the reason might be, I know that he has had multiple contracts since 2010, either because of real contract extensions or because of restructured contracts. Each time there is a signing bonus with the contract, and that gives the player a lot of money in the hand right now, and the team some salary cap relief (that is the basic reasons for restructuring contracts). The result is that everyone got happy, and even though you are right that Tom Brady could have demanded more money throughout his career, I can guarantee you that he does not work cheap relatively to all quarterbacks and he has not given up on a single penny of what is his according to the contracts.
You also mention Aaron Rodgers and Ben Roethlisberger. Both have contracts running through 2019, and you are right that their contracts haven’t given the teams a huge cap hit the last couple of years. That said, both contract is backloaded, meaning that those players are owed a huge amount of money by their team, and there is absolutely no doubt that they will collect all of it. I don’t know how they will do it, and those teams might be able to find a way around the salary cap-ramifications, but usually it is not in a team’s interest to backload contracts that much.
Another point I would like to make is that Aaron Rodgers last got a contract extension in 2013 while Roethlisberger got his current deal in 2015. Much has changed since then. Both players could be up for contract extensions this offseason which could either give the teams more salary cap relief now and even bigger expenses later, or it could kind of even out the payout and thus affect the level of players on the teams in the coming years.
My overall point with this post is to say that, like I wrote in the post you quote, the salary cap is fairly easy to manipulate. You can pretty much structure it any way you want. This makes it possible to put together contracts in ways so that you control how it will affect your salary cap. It takes two parties to make it work, and there are advantages and disadvantages for both parties no matter how the contracts are constructed, and that’s probably why we don’t see every team do it the same way.
As a conclusion, I think the most important thing to know on this specific topic is that the salary cap is nothing more than a tool that, while you can’t ignore it, you can put together any way you want without making your most important players sacrifice anything.